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\hypersetup{
            pdftitle={Europeean Materials Modelling Ontology},
            pdfauthor={Emanuele Ghedini, Gerhard Goldbeck, Adham Hashibon, Georg Schmitz, Jesper Friis},
            pdfkeywords={EMMO, materials science, modelling, characterisation, materials, ontology},
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\title{Europeean Materials Modelling Ontology}
\author{Emanuele Ghedini \and Gerhard Goldbeck \and Adham Hashibon \and Georg Schmitz \and Jesper Friis}
\providecommand{\institute}[1]{}
\institute{European Materials Modelling Counsil (EMMC)}
\date{December 27, 2019}

\begin{document}
%\maketitle
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\begin{titlepage}
  \centering
      {\huge\bfseries Europeean Materials Modelling Ontology\par}\vspace{0.4cm}
        {\scshape\LARGE Version 0.9.10\par}\vspace{1cm}
    \par
    {\Large European Materials Modelling Counsil (EMMC)\par}\vspace{0.2cm}
    %  %{\itshape By Emanuele Ghedini, Gerhard Goldbeck, Adham Hashibon, Georg Schmitz, Jesper Friis\par}\vspace{0.3cm}
  %  \par
    \includegraphics[width=0.12\textwidth]{figs/emmc-logo.png}\par\vspace{1cm}
      {\large December 27, 2019\par}\vspace{2cm}
      \includegraphics{figs/emmo-multidisciplinary.png}\par\vspace{0.5cm}
  \end{titlepage}
\thispagestyle{empty}
\begin{abstract}
EMMO is an ontology that is created by the Europeean Materials Modelling
Council (EMMC) to provide a formal way to describe the fundamental
concepts of physics, chemistry and materials science. EMMO is designed
to pave the road for semantic interoperability providing a generic
common ground for describing materials, models and data that can be
adapted by all domains.

It is a representational framework of predefined classes and axioms
(ontology) provided by experts (EMMC) that enables end users (industry,
research, academy) to represent real life physical entities (materials,
devices), models and properties using ontological signs (individuals) in
a standard way to facilitate interactions and exchanges (data, software,
knowledge) between all involved material modelling and characterization
communities and stakeholders.
{%
  \par\vspace{1cm}
  {\bf Keywords:} EMMO, materials science, modelling, characterisation, materials, ontology
}
{
  \par\vspace{4cm}
  \raggedleft
  Authors:\par
  \itshape
  Emanuele Ghedini, University of Bologne\par Gerhard Goldbeck, Goldbeck Consulting\par Adham Hashibon, Fraunhofer IWM\par Georg Schmitz, ACCESS\par Jesper Friis, SINTEF\par 
}
\end{abstract}

{
\hypersetup{linkcolor=}
\setcounter{tocdepth}{1}
\tableofcontents
}
\hypertarget{introduction}{%
\chapter{Introduction}\label{introduction}}

EMMO is a multidisciplinary effort to develop a standard
representational framework (the ontology) based on current materials
modelling knowledge, including physical sciences, analytical philosophy
and information and communication technologies. This multidisciplinarity
is illustrated by the figure on the title page. It provides the
connection between the physical world, materials characterisation world
and materials modelling world.

\begin{figure}
\centering
\includegraphics[width=6.45833in,height=\textheight]{figs/emmo-three_worlds.png}
\caption{EMMO provides the connection between the physical world,
materials characterisation world and materials modelling world.}
\end{figure}

EMMO is based on and is consistent with the
\href{https://publications.europa.eu/en/publication-detail/-/publication/ec1455c3-d7ca-11e6-ad7c-01aa75ed71a1}{Review
of Materials Modelling},
\href{https://www.cen.eu/news/workshops/Pages/WS_2016-013.aspx}{CEN
Workshop Agreement} and
\href{https://emmc.info/moda-workflow-templates/}{MODA template}.
However, while these efforts are written for humans, EMMO is defined
using the \href{https://en.wikipedia.org/wiki/Web_Ontology_Language}{Web
Ontology Language (OWL)}, which is machine readable and allows for
machine reasoning. In terms of semantic representation, EMMO brings
everything to a much higher level.

As illustrated in the figure below, EMMO covers all aspects of materials
modelling and characterisation, including:

\begin{itemize}
\tightlist
\item
  the \textbf{material} itself, which must be described in a rigorous
  way
\item
  the \textbf{observation process} involving an observer that percieves
  the real world
\item
  the \textbf{properties} that is measured or modelled
\item
  the \textbf{physics laws} that describes the material behaviour
\item
  the \textbf{physical models} that approximate the physics laws
\item
  the \textbf{solver} including the numerical discretisation method that
  leads to a solvable mathematical representation under certain
  simplifying assumptions
\item
  the \textbf{numerical solver} that performs the calculations
\item
  the \textbf{post processing} of experimental or simulated data
\end{itemize}

\begin{figure}
\centering
\includegraphics[width=2.70833in,height=\textheight]{figs/emmo-scope.png}
\caption{The aspects of materials modelling and characterisation covered
by EMMO.}
\end{figure}

\hypertarget{what-is-an-ontology}{%
\section{What is an ontology}\label{what-is-an-ontology}}

In short, an ontology is a specification of a conceptualization. The
word \emph{ontology} has a long history in philosophy, in which it
refers to the subject of existence. The so-called
\href{https://en.wikipedia.org/wiki/Ontological_argument}{ontological
argument} for the existence of God was proposed by Anselm of Canterbury
in 1078. He defined God as \emph{``that than which nothing greater can
be thought''}, and argued that \emph{``if the greatest possible being
exists in the mind, it must also exist in reality. If it only exists in
the mind, then an even greater being must be possible -- one which
exists both in the mind and in reality''}. Even though this example has
little to do with todays use of ontologies in computer science, it
illustrates the basic idea; the ontology defines some basic premises
(concepts and relations between them) from which it is possible reason
to gain new knowledge.

For a more elaborated and modern definition of the ontology we refer the
reader to the one provided by
\href{http://tomgruber.org/writing/ontology-definition-2007.htm}{Tom
Gruber (2009)}. Another useful introduction to ontologies is the paper
\href{http://www.ksl.stanford.edu/people/dlm/papers/ontology-tutorial-noy-mcguinness-abstract.html}{Ontology
Development 101: A Guide to Creating Your First Ontology} by Noy and
McGuinness (2001), which is based on the
\href{https://protege.stanford.edu/}{Protege} sortware, with which EMMO
has been developed.

A taxonomy is a hierarchical representation of classes and subclasses
connected via \texttt{is\_a} relations. Hence, it is a subset of the
ontology excluding all, but the \texttt{is\_a} relations. The main use
of taxonomies are for classifications. The figure shows a simple example
of a taxonomy illustrating a categorisation of four classes into a
hierarchy of more higher of levels of generality.

\begin{figure}
\centering
\includegraphics[width=2.5in,height=\textheight]{figs/animal.png}
\caption{Example of a taxonomy.}
\end{figure}

In EMMO is the taxonomy a rooted directed acyclic graph (DAG). This is
an important since many classification methods relies on this property,
see e.g. \href{https://arxiv.org/abs/1406.4472}{Valentini (2014)} and
\href{https://www.google.no/url?sa=t\&rct=j\&q=\&esrc=s\&source=web\&cd=2\&ved=0ahUKEwi_2vv-8tXbAhUFiiwKHVRdD4EQFgg1MAE\&url=https\%3A\%2F\%2Fwww.springer.com\%2Fcda\%2Fcontent\%2Fdocument\%2Fcda_downloaddocument\%2F9783319202471-c2.pdf\%3FSGWID\%3D0-0-45-1510685-p177420182\&usg=AOvVaw39c3v4a5PfVMEYDulWpF3w}{Robison
et al (2015)}. Note, that EMMO is a DAG does not prevent some classes
from having more than one parent. A \texttt{quantitative\_property} is
for instance both \texttt{formed} and an \texttt{objective\_property}.
See \protect\hyperlink{appendix}{appendix} for the full EMMO taxonomy.

\hypertarget{primitive-elements-in-emmo}{%
\section{Primitive elements in EMMO}\label{primitive-elements-in-emmo}}

\begin{figure}
\centering
\includegraphics[width=6.45833in,height=\textheight]{figs/emmo-primitives.png}
\caption{The primitive building blocks of EMMO.}
\end{figure}

\hypertarget{individuals}{%
\subsection{Individuals}\label{individuals}}

Individuals are the basic, ``ground level'' components of EMMO. They may
include concrete objects such as cars, flowers, stars, persons and
molecules, as well as abstract individuals such as a measured height, a
specific equation and software programs.

Individuals are not simple, but possess attributes in form of axioms
that are defined by the user (interpreter) upon declaration.

\hypertarget{classes}{%
\subsection{Classes}\label{classes}}

Classes represents concepts. They are the building blocks that we use to
create an ontology as a representation of knowledge. We distinguish
between \emph{defined} and \emph{non-defined} classes.

Defined classes are defined by the requirements for being a member of
the class. In the graphical representations of EMMO, defined classes are
orange. For instance, in the graph of the top-level entity branch below,
\texttt{set} and \texttt{abstract} are defined classes. \texttt{set} is
defined via the \texttt{has\_member} relationship, while
\texttt{abstract} is defined via the \texttt{has\_abstract\_part}
relationship.

Non-defined classes are defined as an abstract group of objects, whos
members are defined as belonging to the class. They are yellow in the
graphical representations.

\begin{figure}
\centering
\includegraphics[width=2.5625in,height=\textheight]{figs/entity_branch.png}
\caption{Example of the top-level entity branch showing some classes and
relationships between them.}
\end{figure}

\hypertarget{axioms}{%
\subsection{Axioms}\label{axioms}}

Axioms are propositions in a logical framework that define the relations
between the individuals and classes. They are used to categorise
individuals in classes and to define the \emph{defined} classes.

The simplest form of a class axiom is a class description that just
states the existence of the class and gives it an unique identifier. In
order to provide more knowledge about the class, class axioms typically
contain additional components that state necessary and/or sufficient
characteristics of the class. OWL contains three language constructs for
combining class descriptions into class axioms:

\begin{itemize}
\item
  \texttt{rdfs:subClassOf} allows one to say that the class extension of
  a class description is a subset of the class extension of another
  class description.
\item
  \texttt{owl:equivalentClass} allows one to say that a class
  description has exactly the same class extension as another class
  description.
\item
  \texttt{owl:disjointWith} allows one to say that the class extension
  of a class description has no members in common with the class
  extension of another class description.
\end{itemize}

See the section about \protect\hyperlink{description-logic}{Description
logic} for more information about these language constructs. Axioms are
also used to define relations between relations. These are further
detailed in the chapter on {[}Relations{]}.

\hypertarget{theoretical-foundations}{%
\section{Theoretical foundations}\label{theoretical-foundations}}

EMMO build upon several theoretical frameworks.

\hypertarget{semiotics}{%
\subsection{Semiotics}\label{semiotics}}

Semiotics is the study of meaning-making. It is the dicipline of
formulating something that possibly can exists in a defined space and
time in the real world. It is introdused in EMMO via the \texttt{semion}
class and used as a way to reduce the complexity of a physical to a
simple sign (symbol). A \texttt{semion} is a physical entity that
represents an abstract object.

\hypertarget{set-theory}{%
\subsection{Set theory}\label{set-theory}}

Set theory is the theory of membership. This is introduced via the
\texttt{set} class, representing the collection of all individuals
(signs) that represents a collection of items. Sets are defined via the
\texttt{has\_member} / \texttt{is\_member\_of} relations.

\hypertarget{mereology}{%
\subsection{Mereology}\label{mereology}}

Mereology is the science of parthood. It is introdused via the
\texttt{item} class and based on the mereological \texttt{has\_part} /
\texttt{is\_part\_of} relations.

EMMO makes a strong distinction between membership and parthood
relations. In contrast to sets, items can only have parts that are
themselves items. This means for instance that parthood is only between
substrates of the same dimensionality. Hence, the boundary of an item is
not a part of the item since it has a lower dimensionality.

For further information, see
\href{https://mitpress.mit.edu/books/parts-and-places}{Casati and Varzi
``Parts and Places'' (1999)}.

\hypertarget{topology}{%
\subsection{Topology}\label{topology}}

Topology is the study of geometrical properties and spatial (and
time-wise) relations. It is introdused in combination with mereology
(and therefore often referred to as \textbf{mereotopology}) via the
\texttt{substrate} class, which represents the place in space and time
in which every real world item exists. Substrates in EMMO are always
topologically connedted in space and time.

Mereotopological relationships are defined with the \texttt{encloses} /
\texttt{is\_enclosed\_by} relations.

\hypertarget{metrology}{%
\subsection{Metrology}\label{metrology}}

Metrology is the science of measurements. It is used to introduce units
and link them to properties.

\hypertarget{description-logic}{%
\subsection{Description logic}\label{description-logic}}

\href{https://en.wikipedia.org/wiki/Description_logic}{Description logic
(DL)} is a formal knowledge representation language in which the
\emph{axioms} are expressed. It is less expressive than
\href{https://en.wikipedia.org/wiki/First-order_logic}{first-order logic
(FOL)}, but commonly used for providing the logical formalism for
ontologies and semantic web. EMMO is expressed in the
\href{https://en.wikipedia.org/wiki/Web_Ontology_Language}{Web Ontology
Language (OWL)}, which is in turn is based on DL. This opens for
features like reasoning.

Since it is essential to have a basic notion of OWL and DL, we include
here a very brief overview. For a proper introduction to OWL and DL, we
refer the reader to sources like
\href{http://www.cs.ox.ac.uk/boris.motik/pubs/ghmppss08next-steps.pdf}{Grau
et.al. (2008)}, \href{https://www.w3.org/TR/owl2-primer/}{OWL2 Primer}
and \href{https://www.w3.org/TR/owl-ref/}{OWL Reference}.

OWL distinguishes six between types of class descriptions:

\begin{enumerate}
\def\labelenumi{\arabic{enumi}.}
\tightlist
\item
  a class identifier (a IRI reference)
\item
  an exhaustive enumeration of individuals that together form the
  instances of a class (\texttt{owl:oneOf})
\item
  a property restriction (\texttt{owl:someValuesFrom},
  \texttt{owl:allValuesFrom}, \texttt{owl:hasValue},
  \texttt{owl:cardinality}, \texttt{owl:minCardinality},
  \texttt{owl:maxCardinality})
\item
  the intersection of two or more class descriptions
  (\texttt{owl:intersectionOf})
\item
  the union of two or more class descriptions (\texttt{owl:unionOf})
\item
  the complement of a class description (\texttt{owl:complementOf})
\end{enumerate}

Except for the first, all of these refer to \emph{defined classes}. The
table below shows the notation in OWL, DL and the
\href{http://ceur-ws.org/Vol-216/submission_9.pdf}{Manchester OWL
syntax}, all commonly used for the definitions. The Manchester syntax is
used by \href{https://protege.stanford.edu/}{Protege} and is designed to
not use DL symbols and to be easy and quick to read and write. Several
other syntaxes exists for DL. An interesting example is the pure Python
syntax proposed by
\href{http://www.lesfleursdunormal.fr/_downloads/article_owlready_aim_2017.pdf}{Lamy
(2017)}, which is used in the open source
\href{https://pythonhosted.org/Owlready2/}{Owlready2} Python package.

\begin{longtable}[]{@{}lllll@{}}
\caption{Notation for DL and Protege. A and B are classes, R is an
active relation, S is an passive relation, i and j are individuals and n
is a literal.}\tabularnewline
\toprule
\begin{minipage}[b]{0.18\columnwidth}\raggedright
OWL constructor\strut
\end{minipage} & \begin{minipage}[b]{0.16\columnwidth}\raggedright
DL\strut
\end{minipage} & \begin{minipage}[b]{0.17\columnwidth}\raggedright
Manchester\strut
\end{minipage} & \begin{minipage}[b]{0.20\columnwidth}\raggedright
Read\strut
\end{minipage} & \begin{minipage}[b]{0.14\columnwidth}\raggedright
Meaning\strut
\end{minipage}\tabularnewline
\midrule
\endfirsthead
\toprule
\begin{minipage}[b]{0.18\columnwidth}\raggedright
OWL constructor\strut
\end{minipage} & \begin{minipage}[b]{0.16\columnwidth}\raggedright
DL\strut
\end{minipage} & \begin{minipage}[b]{0.17\columnwidth}\raggedright
Manchester\strut
\end{minipage} & \begin{minipage}[b]{0.20\columnwidth}\raggedright
Read\strut
\end{minipage} & \begin{minipage}[b]{0.14\columnwidth}\raggedright
Meaning\strut
\end{minipage}\tabularnewline
\midrule
\endhead
\begin{minipage}[t]{0.18\columnwidth}\raggedright
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright
\(A\doteq B\)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright
?\strut
\end{minipage} & \begin{minipage}[t]{0.20\columnwidth}\raggedright
A is defined to be equal to B\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright
Class \emph{definition}\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.18\columnwidth}\raggedright
rdf:subclassOf\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright
\(A\sqsubseteq B\)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright
A subclass\_of B\strut
\end{minipage} & \begin{minipage}[t]{0.20\columnwidth}\raggedright
all A are B\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright
Class \emph{inclusion}\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.18\columnwidth}\raggedright
owl:equivalentTo\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright
\(A\equiv B\)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright
A equivalent\_to B\strut
\end{minipage} & \begin{minipage}[t]{0.20\columnwidth}\raggedright
A is equivalent to B\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright
Class \emph{equivalence}\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.18\columnwidth}\raggedright
owl:intersectionOf\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright
\(A\sqcap B\)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright
A and B\strut
\end{minipage} & \begin{minipage}[t]{0.20\columnwidth}\raggedright
A and B\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright
Class \emph{intersection} (\emph{conjunction})\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.18\columnwidth}\raggedright
owl:unionOf\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright
\(A\sqcup B\)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright
A or B\strut
\end{minipage} & \begin{minipage}[t]{0.20\columnwidth}\raggedright
A or B\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright
Class \emph{union} (\emph{disjunction})\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.18\columnwidth}\raggedright
owl:complementOf\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright
\(\lnot A\)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright
not A\strut
\end{minipage} & \begin{minipage}[t]{0.20\columnwidth}\raggedright
not A\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright
Class \emph{complement} (\emph{negation})\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.18\columnwidth}\raggedright
owl:oneOf\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright
\(\{a, b, ...\}\)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright
\{a, b, \ldots{}\}\strut
\end{minipage} & \begin{minipage}[t]{0.20\columnwidth}\raggedright
one of a, b, \ldots{}\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright
Class \emph{enumeration}\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.18\columnwidth}\raggedright
rdf:type\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright
\(a:A\)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright
a is\_a A\strut
\end{minipage} & \begin{minipage}[t]{0.20\columnwidth}\raggedright
a is a A\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright
Class \emph{assertion}\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.18\columnwidth}\raggedright
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright
\((a,b):R\)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright
a object property assertion b\strut
\end{minipage} & \begin{minipage}[t]{0.20\columnwidth}\raggedright
a is R-related to b\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright
Property \emph{assertion}\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.18\columnwidth}\raggedright
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright
\((a,n):R\)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright
a data property assertion n\strut
\end{minipage} & \begin{minipage}[t]{0.20\columnwidth}\raggedright
a is R-related to n\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright
Data \emph{assertion}\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.18\columnwidth}\raggedright
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright
\(\top\)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright
?\strut
\end{minipage} & \begin{minipage}[t]{0.20\columnwidth}\raggedright
top\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright
A special class with every individual as an instance\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.18\columnwidth}\raggedright
\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright
\(\bot\)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright
?\strut
\end{minipage} & \begin{minipage}[t]{0.20\columnwidth}\raggedright
bottom\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright
The empty class\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.18\columnwidth}\raggedright
owl:allValuesFrom\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright
\(\forall R.A\)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright
R only A\strut
\end{minipage} & \begin{minipage}[t]{0.20\columnwidth}\raggedright
all A with R\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright
\href{https://en.wikipedia.org/wiki/Universal_quantifier}{\emph{Universal
restriction}}\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.18\columnwidth}\raggedright
owl:someValuesFrom\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright
\(\exists R.A\)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright
R some A\strut
\end{minipage} & \begin{minipage}[t]{0.20\columnwidth}\raggedright
some A with R\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright
\href{https://en.wikipedia.org/wiki/Universal_quantifier}{\emph{Existential
restriction}}\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.18\columnwidth}\raggedright
owl:cardinality\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright
\(=n R.A\)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright
R exactly n A\strut
\end{minipage} & \begin{minipage}[t]{0.20\columnwidth}\raggedright
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright
\emph{Cardinality restriction}\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.18\columnwidth}\raggedright
owl:minCardinality\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright
\(\leq n R.A\)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright
R min n A\strut
\end{minipage} & \begin{minipage}[t]{0.20\columnwidth}\raggedright
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright
\emph{Minimum cardinality restriction}\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.18\columnwidth}\raggedright
owl:maxCardinality\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright
\(\geq n R.A\)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright
R max n A\strut
\end{minipage} & \begin{minipage}[t]{0.20\columnwidth}\raggedright
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright
\emph{Minimum cardinality restriction}\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.18\columnwidth}\raggedright
owl:hasValue\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright
\(\exists R\{a\}\)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright
R value a\strut
\end{minipage} & \begin{minipage}[t]{0.20\columnwidth}\raggedright
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.18\columnwidth}\raggedright
rdfs:domain\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright
\(\exists R.\top \sqsubseteq A\)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright
R domain A\strut
\end{minipage} & \begin{minipage}[t]{0.20\columnwidth}\raggedright
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.18\columnwidth}\raggedright
rdfs:range\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright
\(\top\sqsubseteq \forall R.A\)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright
R range A\strut
\end{minipage} & \begin{minipage}[t]{0.20\columnwidth}\raggedright
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright
\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.18\columnwidth}\raggedright
owl:inverseOf\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright
\(S\equiv R^-\)\strut
\end{minipage} & \begin{minipage}[t]{0.17\columnwidth}\raggedright
S inverse\_of R\strut
\end{minipage} & \begin{minipage}[t]{0.20\columnwidth}\raggedright
S is inverse of R\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright
Property \emph{inverse}\strut
\end{minipage}\tabularnewline
\bottomrule
\end{longtable}

\hypertarget{examples}{%
\subsubsection{Examples}\label{examples}}

Here are some examples of different class descriptions using both the DL
and Manchester notation.

\hypertarget{inclusion-rdfsubclassof}{%
\paragraph{\texorpdfstring{Inclusion
(\texttt{rdf:subclassOf})}{Inclusion (rdf:subclassOf)}}\label{inclusion-rdfsubclassof}}

Inclusion (\(sqsubseteq\)) defines necessary conditions. Necessary and
sufficient (\(\equiv\)) conditions defined with equivalence.

An employee is a person.

\textbf{DL:} \texttt{employee} \(sqsubseteq\) \texttt{person}

\textbf{Manchester:} \texttt{employee\ is\_a\ person}

\hypertarget{enumeration-owloneof}{%
\paragraph{\texorpdfstring{Enumeration
(\texttt{owl:oneOf})}{Enumeration (owl:oneOf)}}\label{enumeration-owloneof}}

The color of a wine is either white, rose or red:

\textbf{DL:} \texttt{wine\_color} \(\equiv\) \{\texttt{white},
\texttt{rose}, \texttt{red}\}

\textbf{Manchester:}
\texttt{wine\_color\ equivalent\_to\ \{white,\ rose,\ red\}}

\hypertarget{property-restriction-owlsomevaluesfrom}{%
\paragraph{\texorpdfstring{Property restriction
(\texttt{owl:someValuesFrom})}{Property restriction (owl:someValuesFrom)}}\label{property-restriction-owlsomevaluesfrom}}

A mother is a woman that has a child (some person):

\textbf{DL:} \texttt{mother} \(\equiv\) \texttt{woman} \(\sqcap\)
\(\exists\)\texttt{has\_child}.\texttt{person}

\textbf{Manchester:}
\texttt{mother\ equivalent\_to\ woman\ and\ has\_child\ some\ person}

\hypertarget{property-restriction-owlallvaluesfrom}{%
\paragraph{\texorpdfstring{Property restriction
(\texttt{owl:allValuesFrom})}{Property restriction (owl:allValuesFrom)}}\label{property-restriction-owlallvaluesfrom}}

All parents that only have daughters:

\textbf{DL:} \texttt{parents\_with\_only\_daughters} \(\equiv\)
\texttt{person} \(\sqcap\) \(\forall\)\texttt{has\_child}.\texttt{woman}

\textbf{Manchester:}
\texttt{parents\_with\_only\_daughters\ equivalent\_to\ person\ and\ has\_child\ only\ woman}

\hypertarget{property-restriction-owlhasvalue}{%
\paragraph{\texorpdfstring{Property restriction
(\texttt{owl:hasValue})}{Property restriction (owl:hasValue)}}\label{property-restriction-owlhasvalue}}

The owl:hasValue restriction allows to define classes based on the
existence of particular property values. There must be at least one
matching property value.

All children of Mary:

\textbf{DL:} \texttt{Marys\_children} \(\equiv\) \texttt{person}
\(\sqcap\) \(\exists\)\texttt{has\_parent}.\{\texttt{Mary}\}

\textbf{Manchester:}
\texttt{Marys\_children\ equivalent\_to\ person\ and\ has\_parent\ value\ Mary}

\hypertarget{property-cardinality-owlcardinality}{%
\paragraph{\texorpdfstring{Property cardinality
(\texttt{owl:cardinality})}{Property cardinality (owl:cardinality)}}\label{property-cardinality-owlcardinality}}

The owl:cardinality restriction allows to define classes based on the
maximum (owl:maxCardinality), minimum (owl:minCardinality) or exact
(owl:cardinality) number of occurences.

A person with one parent:

\textbf{DL:} \texttt{half\_orphant} \(\equiv\) \texttt{person} and
=1\texttt{has\_parent}.\texttt{person}

\textbf{Manchester:}
\texttt{half\_orphant\ equivalent\_to\ person\ and\ has\_parent\ exactly\ 1\ person}

\hypertarget{intersection-owlintersectionof}{%
\paragraph{\texorpdfstring{Intersection
(\texttt{owl:intersectionOf})}{Intersection (owl:intersectionOf)}}\label{intersection-owlintersectionof}}

Individuals of the intersection of two classes, are simultaneously
instances of both classes.

A man is a person that is male:

\textbf{DL:} \texttt{man} \(\equiv\) \texttt{person} \(\sqcap\)
\texttt{male}

\textbf{Manchester:} \texttt{man\ equivalent\_to\ person\ and\ male}

\hypertarget{union-owlunionof}{%
\paragraph{\texorpdfstring{Union
(\texttt{owl:unionOf})}{Union (owl:unionOf)}}\label{union-owlunionof}}

Individuals of the union of two classes, are either instances of one or
both classes.

A person is a man or woman:

\textbf{DL:} \texttt{person} \(\equiv\) \texttt{man} \(\sqcup\)
\texttt{woman}

\textbf{Manchester:} \texttt{person\ equivalent\_to\ man\ or\ woman}

\hypertarget{complement-owlcomplementof}{%
\paragraph{\texorpdfstring{Complement
(\texttt{owl:complementOf})}{Complement (owl:complementOf)}}\label{complement-owlcomplementof}}

Individuals of the complement of a class, are all individuals that are
not member of the class.

Not a man:

\textbf{DL:} \texttt{female} \(\equiv\) \(\lnot\) \texttt{male}

\textbf{Manchester:} \texttt{female\ equivalent\_to\ not\ male}

\hypertarget{emmo-structure}{%
\section{EMMO Structure}\label{emmo-structure}}

EMMO is structures in a hierarchical set of modules covering all aspects
materials modelling. The modules and their interdependencies are shows
in the figure below. Each module correspond to a separate OWL file. The
special module \texttt{emmo-all.owl} includes all of EMMO.

\begin{figure}
\centering
\includegraphics[width=4.16667in,height=\textheight]{figs/emmo-structure.png}
\caption{EMMO modules.}
\end{figure}

\hypertarget{emmo-core}{%
\subsection{EMMO Core}\label{emmo-core}}

EMMO core contains three levels as illustrated in the figure below.

\begin{figure}
\centering
\includegraphics[width=1.875in,height=\textheight]{figs/emmo-core.png}
\caption{Toplevel structure of EMMO Core.}
\end{figure}

\begin{itemize}
\item
  \textbf{The abstract conceptual level} makes a clear separation
  between \texttt{set} (set theory) and \texttt{item} (mereotopology).
\item
  \textbf{The geometric/topological level} contains the space (3D) and
  time (1D) in which all items unfolds.
\item
  \textbf{The physical level} holds the 4D \texttt{spacetime} in which
  all real world entities exists. A \texttt{spacetime} that can be
  perceived by (interact with) the interpreater is a \texttt{physical}.
  If the \texttt{spacetime} entity is empty in terms of perception, it
  is a \texttt{void}.
\end{itemize}

EMMO defines a parthood hierachy under \texttt{physical} by introducing
the following concepts (illustrated in the figure below):

\begin{itemize}
\item
  \textbf{\texttt{elementary}} is the fundamental, non-divisible
  constituent of entities
\item
  \textbf{\texttt{state}} is a \texttt{physical}whose parts have a
  constant cardinality during its life time
\item
  \textbf{\texttt{existent}} is a succession of states
\end{itemize}

\begin{figure}
\centering
\includegraphics[width=5.20833in,height=\textheight]{figs/physical.png}
\caption{Parthood hierachy under \texttt{physical}.}
\end{figure}

Via the mereological direct parthood relation, EMMO can describe
entities made of parts at different levels of granularity. This is
paramount for cross scale interoperability. Every material in EMMO is
placed on a granularity level and the ontology gives information about
the direct upper and direct lower level classes using the non-transitive
direct parthood relations.

\begin{figure}
\centering
\includegraphics[width=2.29167in,height=\textheight]{figs/emmo-direct_part.png}
\caption{Direct parthood.}
\end{figure}

\hypertarget{emmo-materials}{%
\subsection{EMMO Materials}\label{emmo-materials}}

EMMO Material contains a first draft of a materials ontology. It relies
on direct parthood to identify granularity levels. It is generic and
flexible enough to represent both classical and quantum mechanical
systems in a way that is compatible with different interpretations
(e.g.~the Copenhagen and De Broglie-Bohm interpretations of quantum
mechanics) and levels of approximations (e.g.~classical physics and
Born-Oppenheimer approximation).

\hypertarget{emmo-semiotics}{%
\subsection{EMMO Semiotics}\label{emmo-semiotics}}

The semiotics module introduces three connected branches,
\texttt{symbolic}, \texttt{semiosis} and \texttt{semiotic\_role} in
addition to the \texttt{has\_sign}/\texttt{stands\_for} family of
relations.

Since the EMMO must represent models and properties (which are signs
that stand for a physical entity), the semiotic process must be
described also within the EMMO itself. The concepts of Peirce semiotics
(interpreter, object, sign) are included in the semiotic branch,
together with the semiosis process.

\hypertarget{emmo-formal-languages}{%
\subsection{EMMO Formal languages}\label{emmo-formal-languages}}

\hypertarget{emmo-data-formats}{%
\subsection{EMMO Data formats}\label{emmo-data-formats}}

\hypertarget{emmo-math}{%
\subsection{EMMO Math}\label{emmo-math}}

\hypertarget{emmo-properties}{%
\subsection{EMMO Properties}\label{emmo-properties}}

\hypertarget{emmo-models}{%
\subsection{EMMO Models}\label{emmo-models}}

\hypertarget{emmo-characterisation}{%
\subsection{EMMO Characterisation}\label{emmo-characterisation}}

\hypertarget{how-to-read-this-document}{%
\section{How to read this document}\label{how-to-read-this-document}}

\hypertarget{annotations}{%
\subsection{Annotations}\label{annotations}}

All entities and relations in EMMO have some attributes, called
\emph{annotations}. In many cases, only the necessary \emph{IRI} and
\emph{relations} are provided. However, more descriptive annotations,
like \emph{elucidation} and \emph{comment} will be added with time.
Possible annotations are:

\begin{itemize}
\tightlist
\item
  \textbf{Elucidation} is a human readable explanation and
  clearification of the documented class or relation.
\end{itemize}

\begin{itemize}
\item
  \textbf{Example} clearifies the elucidation through an example. A
  class may have several examples, each addressing different aspects.
\item
  \textbf{Comment} is a clearifying note complementing the definition
  and elucidation. A class may have several comments, each clearifying
  different aspects.
\item
  \textbf{IRI} stands for \emph{international resource identifier}. It
  is an identifier that uniquely identifies the class or relation. IRIs
  are similar to URIs, but are not restricted to the ASCII character
  set. Even though the IRIs used in EMMO appears to be URLs, they
  currently do not point to any existing content. This might change in
  the future.
\item
  \textbf{Relations} is a list of relations applying to the current
  class or relation. The relations for relations are special and will be
  elaborated on in the introduction to chapter {[}Relations{]}. Some of
  the listed relations are defined in the OWL sources, while other are
  inferred by the reasoner.

  The relations are using the Manchester OWL syntax introduced in
  section \protect\hyperlink{description-logic}{Description logic}.
\end{itemize}

\hypertarget{graphs}{%
\subsection{Graphs}\label{graphs}}

The generated graphs borrows some syntax from the
\href{http://www.uml.org/}{Unified Modelling Language (UML)}, which is a
general purpose language for software design and modelling. The table
below shows the style used for the different types of relations and the
concept they corresponds to in UML.

\begin{longtable}[]{@{}lll@{}}
\caption{Notation for arrow styles used in the graphs. Only active
relations are listed. Corresponding passive relations uses the same
style.}\tabularnewline
\toprule
Relation & UML arrow & UML concept\tabularnewline
\midrule
\endfirsthead
\toprule
Relation & UML arrow & UML concept\tabularnewline
\midrule
\endhead
is-a & \includegraphics{figs/arrow-is_a.png} &
inheritance\tabularnewline
disjoint\_with & \includegraphics{figs/arrow-disjoint_with.png} &
association\tabularnewline
equivalent\_to & \includegraphics{figs/arrow-equivalent_to.png} &
association\tabularnewline
encloses & \includegraphics{figs/arrow-relation.png} &
aggregation\tabularnewline
has\_abstract\_part & \includegraphics{figs/arrow-relation.png} &
aggregation\tabularnewline
has\_abstraction & \includegraphics{figs/arrow-relation.png} &
aggregation\tabularnewline
has\_representation & \includegraphics{figs/arrow-relation.png} &
aggregation\tabularnewline
has\_member & \includegraphics{figs/arrow-relation.png} &
aggregation\tabularnewline
has\_property & \includegraphics{figs/arrow-relation.png} &
aggregation\tabularnewline
\bottomrule
\end{longtable}

All relationships have a direction. In the graphical visualisations, the
relationships are represented with an arrow pointing from the subject to
the object. In order to reduce clutter and limit the size of the graphs,
the relations are abbreviated according to the following table:

\begin{longtable}[]{@{}ll@{}}
\caption{Abbriviations of relations used in the graphical representation
of the different subbranches.}\tabularnewline
\toprule
Relation & Abbreviation\tabularnewline
\midrule
\endfirsthead
\toprule
Relation & Abbreviation\tabularnewline
\midrule
\endhead
has\_part only & hp-o\tabularnewline
is\_part\_of only & ipo-o\tabularnewline
has\_member some & hm-s\tabularnewline
is\_member\_of some & imo-s\tabularnewline
has\_abstraction some & ha-s\tabularnewline
is\_abstraction\_of some & iao-s\tabularnewline
has\_abstract\_part only & pap-o\tabularnewline
is\_abstract\_part\_of only & iapo-o\tabularnewline
has\_space\_slice some & hss-s\tabularnewline
is\_space\_slice\_of some & isso-s\tabularnewline
has\_time\_slice some & hts-s\tabularnewline
is\_time\_slice\_of some & itso-s\tabularnewline
has\_projection some & hp-s\tabularnewline
is\_projection\_of some & ipo-s\tabularnewline
has\_proper\_part some & hpp-s\tabularnewline
is\_proper\_part\_of some & ippo-s\tabularnewline
has\_proper\_part\_of some & hppo-s\tabularnewline
has\_spatial\_direct\_part min & hsdp-m\tabularnewline
has\_spatial\_direct\_part some & hsdp-s\tabularnewline
has\_spatial\_direct\_part exactly & hsdp-e\tabularnewline
\bottomrule
\end{longtable}

UML represents classes as a box with three compartment; name, attributes
and operators. However, since the classes in EMMO have no operators and
it gives little meaning to include the OWL annotations as attributes, we
simply represent the classes as boxes.

As already mentioned, defined classes are colored orange, while
undefined classes are yellow.

\hypertarget{emmo-relations}{%
\chapter{EMMO relations}\label{emmo-relations}}

In the language of OWL, relations are called \emph{properties}. However,
since relations describe relations between classes and individuals and
since \protect\hyperlink{Properties}{properties} has an other meaning in
EMMO, we call them \emph{relations} here.

\href{https://en.wikipedia.org/wiki/Resource_Description_Framework}{Resource
Description Framework (RDF)} is a W3C standard that is widely used for
describing informations on the web and is one of the standards that OWL
builds on. RDF expresses information in form of
\emph{subject-predicate-object} triplets. The subject and object are
resources (aka items to describe) and the predicate expresses a
relationship between the subject and the object.

In EMMO, are the subject and object classes or individuals (or data)
while the predicate is a relation. An example of an relationship is the
statement \emph{dog is\_a animal}. Here is \texttt{dog} the subject,
\texttt{is\_a} the predicate and \texttt{animal} the object. We
distinguish between \texttt{active\ relations} where the subject is
acting on the object and \texttt{passive\ relations} where the subject
is acted on by the object.

OWL distingues between \texttt{owl:ObjectProperty} that link classes or
individuals to classes or individuals and \texttt{owl:DatatypeProperty}
that links individuals to data values. Since EMMO only deals with
classes, we will only be discussing object properties. However, in
actual applications build on EMMO, datatype propertyes will be
important.

The characteristics of the different properties is described by the
following \emph{property axioms}:

\begin{itemize}
\item
  \texttt{rdf:subPropertyOf} is used to define that a property is a
  subproperty of some other property. For instance, in the figure below
  showing the relation branch, we see that \texttt{active\_relation} is
  a subproperty or \texttt{relation}.

  The \texttt{rdf:subPropertyOf} axioms forms a taxonomy-like tree for
  relations.
\end{itemize}

\begin{itemize}
\item
  \texttt{owl:equivalentProperty} states that two properties have the
  same property extension.
\item
  \texttt{owl:inverseOf} axioms relate active relations to their
  corresponding passive relations, and vice versa. The root relation
  \texttt{relation} is its own inverse.
\item
  \texttt{owl:FunctionalProperty} is a property that can have only one
  (unique) value y for each instance x, i.e.~there cannot be two
  distinct values y1 and y2 such that the pairs (x,y1) and (x,y2) are
  both instances of this property. Both object properties and datatype
  properties can be declared as ``functional''.
\item
  \texttt{owl:InverseFunctionalProperty}
\item
  \texttt{owl:TransitiveProperty} states that if a pair (x,y) is an
  instance of P, and the pair (y,z) is also instance of P, then we can
  infer the the pair (x,z) is also an instance of P.
\item
  \texttt{owl:SymmetricProperty} states that if the pair (x,y) is an
  instance of P, then the pair (y,x) is also an instance of P.

  A popular example of a symmetric property is the \texttt{friend\_of}
  relation.
\end{itemize}

\hypertarget{emmo_relation-branch}{%
\section{emmo\_relation branch}\label{emmo_relation-branch}}

\begin{figure}
\centering
\includegraphics[width=3.02083in,height=\textheight]{output/html_files/emmo_relation.pdf}
\caption{The emmo\_relation branch.}
\end{figure}

\hypertarget{emmo_relation}{%
\subsection{emmo\_relation}\label{emmo_relation}}

\textbf{Elucidation:} The sign that stand for the most generic EMMO
relation.

\textbf{IRI:}
\url{http://emmc.info/emmo-core\#EMMO_ec2472ae_cf4a_46a5_8555_1556f5a6c3c5}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a owl:ObjectProperty
\item
  is\_a owl:topObjectProperty
\item
  domain \protect\hyperlink{emmo}{emmo}
\item
  range \protect\hyperlink{emmo}{emmo}
\end{itemize}

\hypertarget{mereotopological-branch}{%
\section{mereotopological branch}\label{mereotopological-branch}}

\begin{figure}
\centering
\includegraphics[width=2.91667in,height=\textheight]{output/html_files/mereotopological.pdf}
\caption{The mereotopological branch.}
\end{figure}

\hypertarget{mereotopological}{%
\subsection{mereotopological}\label{mereotopological}}

\textbf{Elucidation:} The generic EMMO mereotopological relation.

\textbf{Comment:} Mereotopology merges mereological and topological
concepts and provides relations between wholes, parts, boundaries, etc.

\textbf{IRI:}
\url{http://emmc.info/emmo-core\#EMMO_03212fd7_abfd_4828_9c8e_62c293052d4b}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a owl:ObjectProperty
\item
  is\_a \protect\hyperlink{emmo_relation}{emmo\_relation}
\end{itemize}

\hypertarget{disconnected}{%
\subsection{disconnected}\label{disconnected}}

\textbf{Elucidation:} The relation between two individuals that stand
for real world topological disconnected objects.

\textbf{IRI:}
\url{http://emmc.info/emmo-core\#EMMO_517dfaf9_4970_41ac_81ee_d031627d2c7c}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a owl:ObjectProperty
\item
  is\_a owl:SymmetricProperty
\item
  is\_a \protect\hyperlink{mereotopological}{mereotopological}
\item
  Inverse(emmo-core.mereotopological)
\end{itemize}

\hypertarget{semiotic-branch}{%
\section{semiotic branch}\label{semiotic-branch}}

\begin{figure}
\centering
\includegraphics[width=5.19792in,height=\textheight]{output/html_files/semiotic.pdf}
\caption{The semiotic branch.}
\end{figure}

\hypertarget{semiotic}{%
\subsection{semiotic}\label{semiotic}}

\textbf{IRI:}
\url{http://emmc.info/emmo-semiotics\#EMMO_2337e25c_3c60_43fc_a8f9_b11a3f974291}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a owl:ObjectProperty
\item
  is\_a \protect\hyperlink{emmo_relation}{emmo\_relation}
\end{itemize}

\hypertarget{connected-branch}{%
\section{connected branch}\label{connected-branch}}

\begin{figure}
\centering
\includegraphics[width=3.5625in,height=\textheight]{output/html_files/connected.pdf}
\caption{The connected branch.}
\end{figure}

\hypertarget{connected}{%
\subsection{connected}\label{connected}}

\textbf{Definition:} Definition: Cxy := x is connected with y

Axiom: 1) Cxx (x is always connected with itself (reflexivity)) Axiom:
2) Cxy-\textgreater{}Cyx (if x is connected with y then y is connected
with x (symmetry))

\textbf{Elucidation:} The relation between two individuals that stand
for real world topological connected objects.

\textbf{Comment:} Causality is a topological property between connected
items.

\textbf{Comment:} Items being connected means that there is a
topological contact or ``interaction'' between them.

\textbf{IRI:}
\url{http://emmc.info/emmo-core\#EMMO_6703954e_34c4_4a15_a9e7_f313760ae1a8}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a owl:ObjectProperty
\item
  is\_a owl:SymmetricProperty
\item
  is\_a \protect\hyperlink{mereotopological}{mereotopological}
\item
  Inverse(emmo-core.mereotopological)
\end{itemize}

\hypertarget{encloses}{%
\subsection{encloses}\label{encloses}}

\textbf{IRI:}
\url{http://emmc.info/emmo-core\#EMMO_8c898653_1118_4682_9bbf_6cc334d16a99}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a owl:ObjectProperty
\item
  is\_a owl:TransitiveProperty
\item
  is\_a \protect\hyperlink{connected}{connected}
\item
  Inverse(emmo-core.connected)
\end{itemize}

\hypertarget{overlaps}{%
\subsection{overlaps}\label{overlaps}}

\textbf{Definition:} Definition: Oxy \textless{}=\textgreater{} ∃z(Pzx ∧
Pzy)

x overlap with y means that there exists a z that is part of both x and
y

\textbf{IRI:}
\url{http://emmc.info/emmo-core\#EMMO_d893d373_b579_4867_841e_1c2b31a8d2c6}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a owl:ObjectProperty
\item
  is\_a owl:SymmetricProperty
\item
  is\_a \protect\hyperlink{connected}{connected}
\item
  Inverse(emmo-core.connected)
\end{itemize}

\hypertarget{overcrosses}{%
\subsection{overcrosses}\label{overcrosses}}

\textbf{IRI:}
\url{http://emmc.info/emmo-core\#EMMO_9cb984ca_48ad_4864_b09e_50d3fff19420}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a owl:ObjectProperty
\item
  is\_a owl:SymmetricProperty
\item
  is\_a \protect\hyperlink{overlaps}{overlaps}
\item
  Inverse(emmo-core.overlaps)
\end{itemize}

\hypertarget{contacts}{%
\subsection{contacts}\label{contacts}}

\textbf{IRI:}
\url{http://emmc.info/emmo-core\#EMMO_4d6504f1_c470_4ce9_b941_bbbebc9ab05d}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a owl:ObjectProperty
\item
  is\_a owl:SymmetricProperty
\item
  is\_a \protect\hyperlink{connected}{connected}
\item
  Inverse(emmo-core.connected)
\end{itemize}

\hypertarget{has_sign-branch}{%
\section{has\_sign branch}\label{has_sign-branch}}

\begin{figure}
\centering
\includegraphics[width=4in,height=\textheight]{output/html_files/has_sign.pdf}
\caption{The has\_sign branch.}
\end{figure}

\hypertarget{has_sign}{%
\subsection{has\_sign}\label{has_sign}}

\textbf{IRI:}
\url{http://emmc.info/emmo-semiotics\#EMMO_60577dea_9019_4537_ac41_80b0fb563d41}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a owl:ObjectProperty
\item
  is\_a \protect\hyperlink{semiotic}{semiotic}
\item
  domain \protect\hyperlink{object}{object}
\item
  range \protect\hyperlink{sign}{sign}
\end{itemize}

\hypertarget{has_convention}{%
\subsection{has\_convention}\label{has_convention}}

\textbf{IRI:}
\url{http://emmc.info/emmo-semiotics\#EMMO_eb3518bf_f799_4f9e_8c3e_ce59af11453b}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a owl:ObjectProperty
\item
  is\_a \protect\hyperlink{has_sign}{has\_sign}
\item
  range \protect\hyperlink{conventional}{conventional}
\end{itemize}

\hypertarget{has_variable}{%
\subsection{has\_variable}\label{has_variable}}

\textbf{IRI:}
\url{http://emmc.info/emmo-math\#EMMO_3446e167_c576_49d6_846c_215bb8878a55}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a owl:ObjectProperty
\item
  is\_a \protect\hyperlink{has_convention}{has\_convention}
\end{itemize}

\hypertarget{has_property}{%
\subsection{has\_property}\label{has_property}}

\textbf{IRI:}
\url{http://emmc.info/emmo-properties\#EMMO_e1097637_70d2_4895_973f_2396f04fa204}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a owl:ObjectProperty
\item
  is\_a \protect\hyperlink{has_convention}{has\_convention}
\item
  range \protect\hyperlink{property}{property}
\end{itemize}

\hypertarget{has_icon}{%
\subsection{has\_icon}\label{has_icon}}

\textbf{IRI:}
\url{http://emmc.info/emmo-semiotics\#EMMO_39c3815d_8cae_4c8f_b2ff_eeba24bec455}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a owl:ObjectProperty
\item
  is\_a \protect\hyperlink{has_sign}{has\_sign}
\item
  range \protect\hyperlink{icon}{icon}
\end{itemize}

\hypertarget{has_model}{%
\subsection{has\_model}\label{has_model}}

\textbf{IRI:}
\url{http://emmc.info/emmo-models\#EMMO_24c71baf_6db6_48b9_86c8_8c70cf36db0c}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a owl:ObjectProperty
\item
  is\_a \protect\hyperlink{has_icon}{has\_icon}
\end{itemize}

\hypertarget{has_index}{%
\subsection{has\_index}\label{has_index}}

\textbf{IRI:}
\url{http://emmc.info/emmo-semiotics\#EMMO_297999d6_c9e4_4262_9536_bd524d1c6e21}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a owl:ObjectProperty
\item
  is\_a \protect\hyperlink{has_sign}{has\_sign}
\item
  range \protect\hyperlink{index}{index}
\end{itemize}

\hypertarget{has_part-branch}{%
\section{has\_part branch}\label{has_part-branch}}

\begin{figure}
\centering
\includegraphics[width=6.95833in,height=\textheight]{output/html_files/has_part.pdf}
\caption{The has\_part branch.}
\end{figure}

\hypertarget{has_part}{%
\subsection{has\_part}\label{has_part}}

\textbf{IRI:}
\url{http://emmc.info/emmo-core\#EMMO_17e27c22_37e1_468c_9dd7_95e137f73e7f}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a owl:ObjectProperty
\item
  is\_a owl:TransitiveProperty
\item
  is\_a \protect\hyperlink{encloses}{encloses}
\item
  is\_a \protect\hyperlink{overlaps}{overlaps}
\item
  Inverse(emmo-core.overlaps)
\end{itemize}

\hypertarget{has_proper_part}{%
\subsection{has\_proper\_part}\label{has_proper_part}}

\textbf{IRI:}
\url{http://emmc.info/emmo-core\#EMMO_9380ab64_0363_4804_b13f_3a8a94119a76}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a owl:ObjectProperty
\item
  is\_a owl:TransitiveProperty
\item
  is\_a \protect\hyperlink{has_part}{has\_part}
\end{itemize}

\hypertarget{has_spatial_part}{%
\subsection{has\_spatial\_part}\label{has_spatial_part}}

\textbf{Elucidation:} A relation that isolates a proper part extending
in time twithin the lifetime of the whole, without covering the full
spatial extension of the 4D whole (i.e.~is not a temporal part).

\textbf{IRI:}
\url{http://emmc.info/emmo-4d\#EMMO_f68030be_94b8_4c61_a161_886468558054}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a owl:ObjectProperty
\item
  is\_a \protect\hyperlink{has_proper_part}{has\_proper\_part}
\end{itemize}

\hypertarget{has_non_essential_part}{%
\subsection{has\_non\_essential\_part}\label{has_non_essential_part}}

\textbf{Elucidation:} A relation that isolates a proper part extending
in time through a portion of the lifetime whole.

\textbf{IRI:}
\url{http://emmc.info/emmo-4d\#EMMO_6e046dd0_9634_4013_b2b1_9cc468087c83}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a owl:ObjectProperty
\item
  is\_a \protect\hyperlink{has_spatial_part}{has\_spatial\_part}
\end{itemize}

\hypertarget{has_essential_part}{%
\subsection{has\_essential\_part}\label{has_essential_part}}

\textbf{Elucidation:} A relation that isolates a proper part extending
in time through all the lifetime of the whole.

\textbf{IRI:}
\url{http://emmc.info/emmo-core\#EMMO_42eef0b0_cc64_4380_b912_8cc37e87506c}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a owl:ObjectProperty
\item
  is\_a owl:TransitiveProperty
\item
  is\_a \protect\hyperlink{has_spatial_part}{has\_spatial\_part}
\end{itemize}

\hypertarget{has_spatial_direct_part}{%
\subsection{has\_spatial\_direct\_part}\label{has_spatial_direct_part}}

\textbf{IRI:}
\url{http://emmc.info/emmo-direct\#EMMO_b2282816_b7a3_44c6_b2cb_3feff1ceb7fe}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a owl:ObjectProperty
\item
  is\_a owl:InverseFunctionalProperty
\item
  is\_a owl:AsymmetricProperty
\item
  is\_a owl:IrreflexiveProperty
\item
  is\_a \protect\hyperlink{has_essential_part}{has\_essential\_part}
\end{itemize}

\hypertarget{has_member}{%
\subsection{has\_member}\label{has_member}}

\textbf{IRI:}
\url{http://emmc.info/emmo-core\#EMMO_6b7276a4_4b9d_440a_b577_0277539c0fc4}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a owl:ObjectProperty
\item
  is\_a owl:AsymmetricProperty
\item
  is\_a owl:IrreflexiveProperty
\item
  is\_a \protect\hyperlink{has_proper_part}{has\_proper\_part}
\item
  domain \protect\hyperlink{collection}{collection}
\item
  range \protect\hyperlink{item}{item}
\end{itemize}

\hypertarget{has_temporal_part}{%
\subsection{has\_temporal\_part}\label{has_temporal_part}}

\textbf{Elucidation:} A relation that isolate a proper part that covers
the total spatial extension of a whole within a time
interval.elucidation

\textbf{IRI:}
\url{http://emmc.info/emmo-core\#EMMO_7afbed84_7593_4a23_bd88_9d9c6b04e8f6}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a owl:ObjectProperty
\item
  is\_a owl:TransitiveProperty
\item
  is\_a \protect\hyperlink{has_proper_part}{has\_proper\_part}
\end{itemize}

\hypertarget{has_temporal_direct_part}{%
\subsection{has\_temporal\_direct\_part}\label{has_temporal_direct_part}}

\textbf{IRI:}
\url{http://emmc.info/emmo-direct\#EMMO_65a2c5b8_e4d8_4a51_b2f8_e55effc0547d}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a owl:ObjectProperty
\item
  is\_a owl:InverseFunctionalProperty
\item
  is\_a owl:AsymmetricProperty
\item
  is\_a owl:IrreflexiveProperty
\item
  is\_a \protect\hyperlink{has_temporal_part}{has\_temporal\_part}
\end{itemize}

\hypertarget{has_direct_part}{%
\subsection{has\_direct\_part}\label{has_direct_part}}

\textbf{IRI:}
\url{http://emmc.info/emmo-direct\#EMMO_a50d920d_1ee3_4668_9a73_5d80a1c6fe15}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a owl:ObjectProperty
\item
  is\_a owl:InverseFunctionalProperty
\item
  is\_a owl:AsymmetricProperty
\item
  is\_a owl:IrreflexiveProperty
\item
  is\_a \protect\hyperlink{has_proper_part}{has\_proper\_part}
\end{itemize}

\hypertarget{has_proper_participant}{%
\subsection{has\_proper\_participant}\label{has_proper_participant}}

\textbf{IRI:}
\url{http://emmc.info/emmo-process\#EMMO_c5aae418_1622_4d02_93c5_21159e28e6c1}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a owl:ObjectProperty
\item
  is\_a \protect\hyperlink{has_proper_part}{has\_proper\_part}
\item
  is\_a \protect\hyperlink{has_participant}{has\_participant}
\end{itemize}

\hypertarget{has_participant}{%
\subsection{has\_participant}\label{has_participant}}

\textbf{IRI:}
\url{http://emmc.info/emmo-process\#EMMO_ae2d1a96_bfa1_409a_a7d2_03d69e8a125a}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a owl:ObjectProperty
\item
  is\_a \protect\hyperlink{has_part}{has\_part}
\item
  domain \protect\hyperlink{process}{process}
\item
  range \protect\hyperlink{participant}{participant}
\end{itemize}

\hypertarget{has_proper_participant-1}{%
\subsection{has\_proper\_participant}\label{has_proper_participant-1}}

\textbf{IRI:}
\url{http://emmc.info/emmo-process\#EMMO_c5aae418_1622_4d02_93c5_21159e28e6c1}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a owl:ObjectProperty
\item
  is\_a \protect\hyperlink{has_proper_part}{has\_proper\_part}
\item
  is\_a \protect\hyperlink{has_participant}{has\_participant}
\end{itemize}

\hypertarget{emmo-classes}{%
\chapter{EMMO classes}\label{emmo-classes}}

\emph{emmo} is a class representing the collection of all the
individuals (signs) that are used in the ontology. Individuals are
declared by the EMMO users when they want to apply the EMMO to represent
the world.

\hypertarget{emmo-branch}{%
\section{emmo branch}\label{emmo-branch}}

The root of all classes used to represent the world. It has two
children; \emph{collection} and \emph{item}.

\emph{collection} is the class representing the collection of all the
individuals (signs) that represents a collection of non-connected real
world objects.

\emph{item} Is the class that collects all the individuals that are
members of a set (it's the most comprehensive set individual). It is the
branch of parthood (mereotopology).

\begin{figure}
\centering
\includegraphics[width=4.33333in,height=\textheight]{output/html_files/emmo.pdf}
\caption{The emmo branch.}
\end{figure}

\hypertarget{emmo}{%
\subsection{emmo}\label{emmo}}

\textbf{Elucidation:} The class representing the collection of all the
individuals declared in this ontology that stand for real world objects.

\textbf{Comment:} `emmo' is the disjoint union of `item' and
`collection' (covering axiom).

The union implies that `emmo' individuals can only be `item' individuals
(standing for self-connected real world objects) or `collection'
individuals (standing for a collection of disconnected items).

Disjointness means that a `collection' individual cannot be an `item'
individual and viceversa, meaning that a real world object cannot be
self-connected and non-self connected at the same time.

\textbf{Comment:} For the EMMO the universe is represented at
meta-ontological level (i.e.~the representational level that includes
the ontologist, the ontology and the universe) as a 4D path-connected
topological manifold (i.e.~the spacetime).

A real world object is then a topological sub-region of the whole 4D
manifold that describes our universe.

A universe sub-region is isolated and defined as a real world object by
the ontologist, through a semiotic process that occurs on the
meta-ontological level.

Mereotopology is the fundamental logical representation used to
characterize the universe and to provide the definitions for the EMMO
concepts.

The fundamental distinction between real world objects upon which the
EMMO is based in self-connectedness: a real world object can be
self-connected xor not self-connected.

\textbf{Comment:} In the EMMO we will refer to spacetime as a Minkowski
space, restricting the ontology to special relativity only. However,
exension to general relativity, will adding more complexity, should not
change the overall approach.

\textbf{Comment:} Parthood relations does not change dimensionality of
an `emmo' individual, i.e.~every part of a real world object always
retains its 4D dimensionality.

It follows that, for the EMMO, real world objects of dimensionality
lower than 4D do not exist (e.g.~surfaces, lines).

\textbf{IRI:}
\url{http://emmc.info/emmo-core\#EMMO_802d3e92_8770_4f98_a289_ccaaab7fdddf}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a owl:Thing
\end{itemize}

\hypertarget{collection}{%
\subsection{collection}\label{collection}}

\textbf{Elucidation:} The class of all individuals that stands for a
real world not self-connected object.

\textbf{Elucidation:} The class representing the collection of all the
individuals (signs) that represents a collection of `item' individuals.

\textbf{Comment:} A `collection' individual is a sign that stands for a
non-self-connected real world object.

A `collection' individual is related to each `item' individuals of the
collection (i.e.~the members) through the membership relation.

An `item' individual stands for a real world self-connected object which
can be represented as a whole made of connected parts (e.g.~a car made
of components).

\textbf{Comment:} A `set' individual cannot be member of a `set' (to
avoid Russel's paradox).

\textbf{Comment:} Formally, `set' is axiomatized as the class of
individuals that `has\_member' some `item'.

A `set' cannot have as member another `set'. This relation is expressed
instead by the subset relation, which is the OWL-DL built-in `is\_a'
relation used to declare subclasses of `set'.

\textbf{Comment:} Since OWL-DL classes are intended as signs that stand
for real world sets, we can consider the `set' branch as a
meta-ontological branch, since `item' class and all its subclasses are
then individuals of `set'.

It is also possible to define a relation `is\_subset\_of' valid only
between `set' individuals that is equivalent to the OWL-DL built-in
`is\_a' relation between classes in the `item' branch.

However this is not done in the EMMO for the sake of simplicity and due
to the limitation of the language.

\textbf{Comment:} The `set' class can be used to declare individuals
that stand for collections of parts that does not form a self-connected
whole in mereotopological sense.

e.g.~the set of users of a particular software, the set of atoms that
have been part of that just dissociated molecule, or even the set of
atoms that are part of a molecule considered as single individual
entities and not as a mereotopological self-connected fusion.

\textbf{IRI:}
\url{http://emmc.info/emmo-core\#EMMO_2d2ecd97_067f_4d0e_950c_d746b7700a31}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{emmo}{emmo}
\item
  (\protect\hyperlink{has_member}{has\_member} some
  \protect\hyperlink{item}{item})
\end{itemize}

\hypertarget{item}{%
\subsection{item}\label{item}}

\textbf{Elucidation:} The class of individuals that stand for single
real world self-connected objects.

\textbf{Elucidation:} The class that collects all the individuals that
are member of a set (it's the most comprehensive set individual).

\textbf{Comment:} A real world object is self-connected if any two parts
that make up the whole are connected to each other (here the concept of
connection is primitive).

Alternatively, using the primitive path-connectivity concept we can
define a self-connected real world object as an object for which each
couple of points is path-connected.

\textbf{Comment:} An `item' individual stands for a real world
self-connected object which can be represented as a whole made of
connected parts (e.g.~a car made of components).

The `item' individuals stand for sub-regions of the 4D spacetime.

In the EMMO, connectivity is the topological foundation of causality.

All physical systems, i.e.~systems whose behaviour is explained by
physics laws, are always represented by `item'-s.

Members of a 'collection" lack of causality connection, i.e.~they do not
constitute a physical system.

\textbf{Comment:} The `item' class and all its sub-classes are `set'
individuals.

The `item' branch will be used to represent the world things and can be
seen in practice as the ontology core.

\textbf{IRI:}
\url{http://emmc.info/emmo-core\#EMMO_eb3a768e_d53e_4be9_a23b_0714833c36de}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{emmo}{emmo}
\end{itemize}

\hypertarget{quantum}{%
\subsection{quantum}\label{quantum}}

\textbf{Elucidation:} An `emmo' that can't be further divided in time
nor in space.

\textbf{Comment:} A `quantum' is the most fundamental subclass of
`item', since we consider it as the smallest self-connected 4D real
world object.

The quantum concept recalls the fact that there is lower epistemological
limit to our knowledge of the universe, related to the uncertainity
principle.

\textbf{Comment:} A quantum is a 4D real world object.

\textbf{Comment:} A quantum is the EMMO mereological a-tomic entity.

To avoid confusion with the concept of atom coming from physics, we will
use the expression quantum mereology, instead of atomistic mereology.

\textbf{IRI:}
\url{http://emmc.info/emmo-core\#EMMO_3f9ae00e_810c_4518_aec2_7200e424cf68}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{item}{item}
\item
  (\protect\hyperlink{has_proper_part}{has\_proper\_part} only
  owl:Nothing)
\end{itemize}

\hypertarget{void}{%
\subsection{void}\label{void}}

\textbf{Definition:} A `item' that has no `physical' parts.

\textbf{IRI:}
\url{http://emmc.info/emmo-core\#EMMO_29072ec4_ffcb_42fb_bdc7_26f05a2e9873}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{item}{item}
\item
  (\protect\hyperlink{has_part}{has\_part} only
  \protect\hyperlink{void}{void})
\end{itemize}

\hypertarget{existent}{%
\subsection{existent}\label{existent}}

\textbf{Definition:} A `item' which is a `state' or made only of `state'
temporal direct parts.

\textbf{Comment:} `existent' is the most important class to be used for
representing real world objects under a reductionistic perspective
(i.e.~objects come from the composition of sub-part objects).

`existent' class collects all individuals that stand for real world
objects that can be structured in temporal sub-parts of constant
mereological cardinality (i.e.~number of parts) through the temporal
direct parthood, that provides a way to axiomatize tassellation
principles for a specific whole class, and non-transitivity to retain
the granularity levels.

e.g.~a car, a supersaturated gas with nucleating nanoparticles, an atom
that becomes ionized and then recombines with an electron.

\textbf{Comment:} IMPORTANT: if we agree that every item can be
partitioned in time into `state'-s with constant cardinality, then
`existent' is conincident with `item'.

\textbf{Comment:} ex-sistere (latin): to stay (to persist through time)
outside others of the same type (to be distinct from the rest).

\textbf{IRI:}
\url{http://emmc.info/emmo-direct\#EMMO_52211e5e_d767_4812_845e_eb6b402c476a}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{physical}{physical}
\item
  is\_a \protect\hyperlink{item}{item}
\item
  is\_a \protect\hyperlink{state}{state} or
  (\protect\hyperlink{has_temporal_direct_part}{has\_temporal\_direct\_part}
  some \protect\hyperlink{state}{state})
\item
  (\protect\hyperlink{has_temporal_direct_part}{has\_temporal\_direct\_part}
  only \protect\hyperlink{state}{state})
\end{itemize}

\hypertarget{physical-branch}{%
\section{physical branch}\label{physical-branch}}

\begin{figure}
\centering
\includegraphics[width=3.89583in,height=\textheight]{output/html_files/physical.pdf}
\caption{The physical branch.}
\end{figure}

\hypertarget{physical}{%
\subsection{physical}\label{physical}}

\textbf{Elucidation:} A `item' that is an `elementary' or has some
`elementary' as proper parts and whose temporal proper parts are only
`physical'-s (i.e.~it can be perceived without interruptions in time).

\textbf{Comment:} A `physical' is the class that contains all the
individuals that stand for real world objects that interact physically
with the interpreter.

Perception is a subcategory of interaction.

A physical must be perceived through physical interaction by the
ontologist. Then the ontologist can declare an individual standing for
the physical object just perceived.

\textbf{Comment:} A `physical' must include at least an `elementary'
part, but can also include void parts.

A `physical' may include as part also the `void' surrounding or enclosed
by its `physical' sub parts.

There are no particular criteria for `physical'-s structure, except that
is made of some `elementary'-s as proper parts and not only `void'.

This is done in order to: a) take into account the quantum nature of
physical systems, in which the actual position of sub-components
(e.g.~electrons in an atom) is not known except for its probability
distribution function (according to the Copenhagen interpretation.) b)
take into account the fact that large entities (e.g.~devices, cars,
materials) have some void into them.

e.g.~a `spacetime' that has spatial parts an atom and a cubic light year
of `void' extending for some time can be a `physical' individual.

\textbf{Comment:} A `physical' with dimensions other than 4D cannot
exist, following the restriction of the parent `emmo' class.

It follows from the fact that perception is always a process (e.g.~it
unfolds in time).

e.g.~you always have an aperture time when you take a picture or measure
a property. Instantaneous perceptions are idealizations (abstractions)
or a very small time measurement.

\textbf{Comment:} In the EMMO there are no relations such as
`occupies\_space', since `physical'-s are themselves the 4D region.

\textbf{Comment:} The EMMO can be used to represent real world entities
as `physical'-s that are easy to connect to classical or quantum
mechanical based models.

Classical mechanics poses no representational issues, for the EMMO: the
4D representation of `physical'-s is consistent with classical physics
systems.

However, the representation of `physical'-s that are typically analized
through quantum mechanics (e.g.~molecules, atoms, clusters), is not
straightforward.

\begin{enumerate}
\def\labelenumi{\arabic{enumi})}
\tightlist
\item
  De Broglie - Bohm interpretation The most simple approach is to rely
  on Bohmian mechanics, in which each particle is supposed to exists in
  a specific position between measurements (hidden variables approach),
  while its trajectory is calculated using a Guiding Equation based on a
  quantum field calculated with the Schroedinger Equation.
\end{enumerate}

While this approach is really easy to implement in an ontology, since
each entity has its own well defined 4D region, its mathematical
representation failed to receive large consensus due to the difficulties
to include relativistic effects, to be extended to subnuclear scale and
the strong non-locality assumtpion of the quantum field.

Nevertheless, the Bohmian mechanics is a numerical approach that is used
in electronic models to reduce the computational effort of the solution
of Schroedinger Equation.

In practice, an EMMO user can declare a `physical' individual that stand
for the whole quantum system to be described, and at the same time all
sub-parts individuals can be declared, having them a well defined
position in time, according to De Broglie - Bohm interpretation. The
Hamiltonian can be calculated by considering the sub-part individuals.

`physical'-s are then made of `physical' parts and `void' parts that
stand for the space between `physical'-s (e.g.~the void between
electrons and nucleus in an atom).

\begin{enumerate}
\def\labelenumi{\arabic{enumi})}
\setcounter{enumi}{1}
\tightlist
\item
  Copenhagen interpretation In this interpretation the properties
  (e.g.~energy level, position, spin) of a particle are not defined in
  the interval between two measurements and the quantum system is
  entangled (i.e.~properties of particles in the sysyem are correlated)
  and described by a global wavefunction obtained solving the
  Schroedinger Equation.
\end{enumerate}

Upon measurement, the wavefunction collapses to a combination of close
eigenstates that provide information about bservables of the system
components (e.g.~position, energy).

The EMMO can be used to represent `physical'-s that can be related to
Copenhagen based models. In practice, the user should follow these
steps:

\begin{enumerate}
\def\labelenumi{\alph{enumi})}
\item
  define the quantum system as a `physical' individual (e.g.~an H2
  molecule) under a specific class (e.g. `h2\_molecule'). This
  individual is the whole.
\item
  define the axioms of the class that describe how many sub-parts are
  expected for the whole and their class types (e.g. `h2\_molecule' has
  axioms `has\_proper\_part exactly 2 electron' and 'has\_proper\_part
  exactly 2 nucleus)
\item
  the user can now connect the whole to a Schroedinger equation based
  model whose Hamiltonian is calculated trough the information coming
  only from the axioms. No individuals are declared for the subparts!
\item
  a measurement done on the quantum system that provides information on
  the sub-part observables is interpreted as wavefunction collapse and
  leads to the end of the whole and the declaration of the sub-parts
  individuals which can be themselves other quantum systems
\end{enumerate}

e.g.~if the outer electron of the H2 molecule interacts with another
entity defining its state, then the whole that stands for the entangled
H2 molecule becomes a `physical' made of an electron individual, a
quantum system made of one electron and two nuclei and the void between
them.

e.g.~in the Born-Oppenheimer approximation the user represent the atom
by un-entangling nucleus and electronic cloud. The un-entanglement comes
in the form of declaration of individual as parts.

e.g.~the double slit experiment can be represent in the EMMO as: a)
before the slit: a `physical' that extend in space and has parts
`electron' and `void', called `single\_electron\_wave\_function'.
`electron' and `void' are only in the axioms and not decalred
individuals. b) during slit passage: a `physical' made of one declared
individual, the `electron'. c) after the slit: again
`single\_electron\_wave\_function' d) upon collision with the detector:
`physical' made of one declared individual, the `electron'.

\textbf{Comment:} The purpose of the `physical' branch is to provide a
representation of the real world objects, while the models used to
explain or predict the behaviour of the real world objects lay under the
`semiotic' branch.

More than one model can be connected to the same `physical'.

e.g.~Navier-Stokes or Euler equation applied to the same fluid

\textbf{IRI:}
\url{http://emmc.info/emmo-core\#EMMO_c5ddfdba_c074_4aa4_ad6b_1ac4942d300d}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{item}{item}
\item
  is\_a \protect\hyperlink{elementary}{elementary} or
  (\protect\hyperlink{has_proper_part}{has\_proper\_part} some
  \protect\hyperlink{physical}{physical})
\item
  (\protect\hyperlink{has_temporal_part}{has\_temporal\_part} only
  \protect\hyperlink{physical}{physical})
\end{itemize}

\hypertarget{participant}{%
\subsection{participant}\label{participant}}

\textbf{Elucidation:} A portion of a `process' that participates to the
`process' with a specific role.

\textbf{Comment:} If we allow a void region to play a role in a process,
the `participant' class must belong to `item'.

\textbf{Comment:} In the EMMO the relation of participation to a process
falls under mereotopology.

\textbf{IRI:}
\url{http://emmc.info/emmo-process\#EMMO_49804605_c0fe_4538_abda_f70ba1dc8a5d}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{physical}{physical}
\end{itemize}

\hypertarget{semiotic-1}{%
\subsection{semiotic}\label{semiotic-1}}

\textbf{Elucidation:} The class of semiotic elements used in Peirce's
semiotic theory.

``Namely, a sign is something, A, which brings something, B, its
interpretant sign determined or created by it, into the same sort of
correspondence with something, C, its object, as that in which itself
stands to C.'' (Peirce 1902, NEM 4, 20--21).

The triadic elements: - `sign': the sign A (e.g.~a name) -
`interpretant': the sign B as the effects of the sign A on the
interpreter (e.g.~the mental concept of what a name means) - `object':
the object C (e.g.~the entity to which the sign A and B refer to)

This class includes also the `interpeter' i.e.~the entity that connects
the `sign' to the `object'

\textbf{IRI:}
\url{http://emmc.info/emmo-semiotics\#EMMO_b803f122_4acb_4064_9d71_c1e5fd091fc9}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{participant}{participant}
\item
  (Inverse(emmo-process.has\_proper\_participant) some
  \protect\hyperlink{semiosis}{semiosis})
\item
  equivalent\_to \protect\hyperlink{interpreter}{interpreter} or
  \protect\hyperlink{object}{object} or \protect\hyperlink{sign}{sign}
\end{itemize}

\hypertarget{object}{%
\subsection{object}\label{object}}

\textbf{Elucidation:} The object, in Peirce semiotics.

\textbf{Comment:} Here is assumed that the concept of `object' is always
relative to a `semiotic' process. An `object' does not exists per se,
but it's always part of an interpretation.

The EMMO relies on strong reductionism, i.e.~everything real is a
formless collection of elementary particles: we give a meaning to real
world entities only by giving them boundaries and defining them using
`sign'-s.

In this way the `sign'-ed entity become and `object', and the `object'
is the basic entity needed in order to apply a logical formalism to the
real world entities (i.e.~we can speak of it through its sign, and use
logics on it through its sign).

\textbf{IRI:}
\url{http://emmc.info/emmo-semiotics\#EMMO_6f5af708_f825_4feb_a0d1_a8d813d3022b}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{semiotic}{semiotic}
\item
  equivalent\_to (\protect\hyperlink{has_sign}{has\_sign} some
  \protect\hyperlink{sign}{sign})
\end{itemize}

\hypertarget{interpreter}{%
\subsection{interpreter}\label{interpreter}}

\textbf{Elucidation:} The entity (or agent, or observer, or cognitive
entity) who connects `sign', `interpretant' and `object'.

\textbf{IRI:}
\url{http://emmc.info/emmo-semiotics\#EMMO_0527413c_b286_4e9c_b2d0_03fb2a038dee}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{semiotic}{semiotic}
\item
  (\protect\hyperlink{has_spatial_part}{has\_spatial\_part} some
  \protect\hyperlink{interpretant}{interpretant})
\end{itemize}

\hypertarget{observer}{%
\subsection{observer}\label{observer}}

\textbf{Elucidation:} An `interpreter' that perceives another `entity'
(the `object') through a specific perception mechanism and produces a
`property' (the `sign') that stands for the result of that particular
perception.

\textbf{IRI:}
\url{http://emmc.info/emmo-properties\#EMMO_1b52ee70_121e_4d8d_8419_3f97cd0bd89c}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{interpreter}{interpreter}
\end{itemize}

\hypertarget{measurement_instrument}{%
\subsection{measurement\_instrument}\label{measurement_instrument}}

\textbf{IRI:}
\url{http://emmc.info/emmo-physical-properties\#EMMO_f2d5d3ad_2e00_417f_8849_686f3988d929}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{observer}{observer}
\end{itemize}

\hypertarget{existent-1}{%
\subsection{existent}\label{existent-1}}

\textbf{Definition:} A `item' which is a `state' or made only of `state'
temporal direct parts.

\textbf{Comment:} `existent' is the most important class to be used for
representing real world objects under a reductionistic perspective
(i.e.~objects come from the composition of sub-part objects).

`existent' class collects all individuals that stand for real world
objects that can be structured in temporal sub-parts of constant
mereological cardinality (i.e.~number of parts) through the temporal
direct parthood, that provides a way to axiomatize tassellation
principles for a specific whole class, and non-transitivity to retain
the granularity levels.

e.g.~a car, a supersaturated gas with nucleating nanoparticles, an atom
that becomes ionized and then recombines with an electron.

\textbf{Comment:} IMPORTANT: if we agree that every item can be
partitioned in time into `state'-s with constant cardinality, then
`existent' is conincident with `item'.

\textbf{Comment:} ex-sistere (latin): to stay (to persist through time)
outside others of the same type (to be distinct from the rest).

\textbf{IRI:}
\url{http://emmc.info/emmo-direct\#EMMO_52211e5e_d767_4812_845e_eb6b402c476a}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{physical}{physical}
\item
  is\_a \protect\hyperlink{item}{item}
\item
  is\_a \protect\hyperlink{state}{state} or
  (\protect\hyperlink{has_temporal_direct_part}{has\_temporal\_direct\_part}
  some \protect\hyperlink{state}{state})
\item
  (\protect\hyperlink{has_temporal_direct_part}{has\_temporal\_direct\_part}
  only \protect\hyperlink{state}{state})
\end{itemize}

\hypertarget{vacuum}{%
\subsection{vacuum}\label{vacuum}}

\textbf{IRI:}
\url{http://emmc.info/emmo-material\#EMMO_3c218fbe_60c9_4597_8bcf_41eb1773af1f}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{physical}{physical}
\item
  equivalent\_to \protect\hyperlink{physical}{physical} and not
  (\protect\hyperlink{has_part}{has\_part} some
  \protect\hyperlink{massive}{massive})
\end{itemize}

\hypertarget{field}{%
\subsection{field}\label{field}}

\textbf{Elucidation:} A `physical' with `massless' parts that are
mediators of interactions.

\textbf{IRI:}
\url{http://emmc.info/emmo-material\#EMMO_70dac51e_bddd_48c2_8a98_7d8395e91fc2}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{physical}{physical}
\item
  equivalent\_to (\protect\hyperlink{has_part}{has\_part} some
  \protect\hyperlink{massless}{massless})
\end{itemize}

\hypertarget{process-branch}{%
\section{process branch}\label{process-branch}}

\begin{figure}
\centering
\includegraphics[width=6.11458in,height=\textheight]{output/html_files/process.pdf}
\caption{The process branch.}
\end{figure}

\hypertarget{process}{%
\subsection{process}\label{process}}

\textbf{Definition:} A `process' is defined as a temporal part of a
`physical' that is categorized in a primitive process subclass according
to what type of process we want to represent.

Following the common definition of process, every `physical' is a
process since every 4D object always has a time dimension. However, in
the EMMO we restrict the meaning of the word process to `physical'-s
whose evolution in time have a particular meaning for the ontologist.

i.e.~a `process' is not only something that unfolds in time (which is
automatically represented in a 4D ontology), but something happening
that has a meaning for the interpreter.

\textbf{Elucidation:} A `process' is always a `physical', since a `void'
does not have elements that evolves in time.

However, `void' parts inside a `process' can be a `participant'.

\textbf{Elucidation:} A temporal part of a `physical' that identifies a
particular type of evolution in time.

\textbf{IRI:}
\url{http://emmc.info/emmo-process\#EMMO_43e9a05d_98af_41b4_92f6_00f79a09bfce}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{physical}{physical}
\item
  (\protect\hyperlink{has_participant}{has\_participant} some
  \protect\hyperlink{participant}{participant})
\end{itemize}

\hypertarget{physical_phenomenon}{%
\subsection{physical\_phenomenon}\label{physical_phenomenon}}

\textbf{IRI:}
\url{http://emmc.info/emmo-models\#EMMO_314d0bd5_67ed_437e_a609_36d46147cea7}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{process}{process}
\end{itemize}

\hypertarget{semiosis}{%
\subsection{semiosis}\label{semiosis}}

\textbf{Elucidation:} A `process', that has participant an
`interpreter', that is aimed to produce a `sign' representing another
participant, the `interpreted'.

\textbf{Example:} Me looking a cat and saying loud: ``Cat!''
-\textgreater{} the semiosis process

me -\textgreater{} interpreter cat -\textgreater{} object (in Peirce
semiotics) the cat perceived by my mind -\textgreater{} interpretant
``Cat!'' -\textgreater{} sign, the produced sign

\textbf{IRI:}
\url{http://emmc.info/emmo-semiotics\#EMMO_008fd3b2_4013_451f_8827_52bceab11841}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{process}{process}
\item
  (\protect\hyperlink{has_participant}{has\_participant} some
  \protect\hyperlink{interpreter}{interpreter})
\item
  (\protect\hyperlink{has_proper_participant}{has\_proper\_participant}
  some \protect\hyperlink{object}{object})
\item
  (\protect\hyperlink{has_proper_participant}{has\_proper\_participant}
  some \protect\hyperlink{sign}{sign})
\end{itemize}

\hypertarget{observation}{%
\subsection{observation}\label{observation}}

\textbf{Elucidation:} A `semiosis' that involves an `observer' that
perceives another `entity' (the `object') through a specific perception
mechanism and produces a `property' (the `sign') that stands for the
result of that particular perception.

\textbf{IRI:}
\url{http://emmc.info/emmo-properties\#EMMO_10a5fd39_06aa_4648_9e70_f962a9cb2069}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{semiosis}{semiosis}
\item
  (\protect\hyperlink{has_participant}{has\_participant} some
  \protect\hyperlink{observer}{observer})
\end{itemize}

\hypertarget{experiment}{%
\subsection{experiment}\label{experiment}}

\textbf{Elucidation:} An experiment is a process that is intended to
replicate a physical phenomenon in a controlled environment.

\textbf{IRI:}
\url{http://emmc.info/emmo-models\#EMMO_22522299_4091_4d1f_82a2_3890492df6db}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{observation}{observation}
\item
  (\protect\hyperlink{has_participant}{has\_participant} some
  \protect\hyperlink{physical_phenomenon}{physical\_phenomenon})
\end{itemize}

\hypertarget{theorization}{%
\subsection{theorization}\label{theorization}}

\textbf{Elucidation:} The `semiosis' process of interpreting a
`physical' and provide a complec sign, `theory' that stands for it and
explain it to another interpreter.

\textbf{IRI:}
\url{http://emmc.info/emmo-models\#EMMO_6c739b1a_a774_4416_bb31_1961486fa9ed}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{observation}{observation}
\end{itemize}

\hypertarget{measurement}{%
\subsection{measurement}\label{measurement}}

\textbf{Elucidation:} An `observation' that results in a quantitative
comparison of a `property' of an `object' with a standard reference.

\textbf{IRI:}
\url{http://emmc.info/emmo-physical-properties\#EMMO_463bcfda_867b_41d9_a967_211d4d437cfb}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{observation}{observation}
\item
  (\protect\hyperlink{has_participant}{has\_participant} some
  \protect\hyperlink{measurement_instrument}{measurement\_instrument})
\end{itemize}

\hypertarget{semiotic-branch-1}{%
\section{semiotic branch}\label{semiotic-branch-1}}

\begin{figure}
\centering
\includegraphics[width=5.19792in,height=\textheight]{output/html_files/semiotic.pdf}
\caption{The semiotic branch.}
\end{figure}

\hypertarget{semiotic-2}{%
\subsection{semiotic}\label{semiotic-2}}

\textbf{IRI:}
\url{http://emmc.info/emmo-semiotics\#EMMO_2337e25c_3c60_43fc_a8f9_b11a3f974291}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a owl:ObjectProperty
\item
  is\_a \protect\hyperlink{emmo_relation}{emmo\_relation}
\end{itemize}

\hypertarget{has_sign-1}{%
\subsection{has\_sign}\label{has_sign-1}}

\textbf{IRI:}
\url{http://emmc.info/emmo-semiotics\#EMMO_60577dea_9019_4537_ac41_80b0fb563d41}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a owl:ObjectProperty
\item
  is\_a \protect\hyperlink{semiotic}{semiotic}
\item
  domain \protect\hyperlink{object}{object}
\item
  range \protect\hyperlink{sign}{sign}
\end{itemize}

\hypertarget{has_convention-1}{%
\subsection{has\_convention}\label{has_convention-1}}

\textbf{IRI:}
\url{http://emmc.info/emmo-semiotics\#EMMO_eb3518bf_f799_4f9e_8c3e_ce59af11453b}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a owl:ObjectProperty
\item
  is\_a \protect\hyperlink{has_sign}{has\_sign}
\item
  range \protect\hyperlink{conventional}{conventional}
\end{itemize}

\hypertarget{has_variable-1}{%
\subsection{has\_variable}\label{has_variable-1}}

\textbf{IRI:}
\url{http://emmc.info/emmo-math\#EMMO_3446e167_c576_49d6_846c_215bb8878a55}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a owl:ObjectProperty
\item
  is\_a \protect\hyperlink{has_convention}{has\_convention}
\end{itemize}

\hypertarget{has_property-1}{%
\subsection{has\_property}\label{has_property-1}}

\textbf{IRI:}
\url{http://emmc.info/emmo-properties\#EMMO_e1097637_70d2_4895_973f_2396f04fa204}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a owl:ObjectProperty
\item
  is\_a \protect\hyperlink{has_convention}{has\_convention}
\item
  range \protect\hyperlink{property}{property}
\end{itemize}

\hypertarget{has_icon-1}{%
\subsection{has\_icon}\label{has_icon-1}}

\textbf{IRI:}
\url{http://emmc.info/emmo-semiotics\#EMMO_39c3815d_8cae_4c8f_b2ff_eeba24bec455}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a owl:ObjectProperty
\item
  is\_a \protect\hyperlink{has_sign}{has\_sign}
\item
  range \protect\hyperlink{icon}{icon}
\end{itemize}

\hypertarget{has_model-1}{%
\subsection{has\_model}\label{has_model-1}}

\textbf{IRI:}
\url{http://emmc.info/emmo-models\#EMMO_24c71baf_6db6_48b9_86c8_8c70cf36db0c}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a owl:ObjectProperty
\item
  is\_a \protect\hyperlink{has_icon}{has\_icon}
\end{itemize}

\hypertarget{has_index-1}{%
\subsection{has\_index}\label{has_index-1}}

\textbf{IRI:}
\url{http://emmc.info/emmo-semiotics\#EMMO_297999d6_c9e4_4262_9536_bd524d1c6e21}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a owl:ObjectProperty
\item
  is\_a \protect\hyperlink{has_sign}{has\_sign}
\item
  range \protect\hyperlink{index}{index}
\end{itemize}

\hypertarget{state-branch}{%
\section{state branch}\label{state-branch}}

\begin{figure}
\centering
\includegraphics[width=6.95833in,height=\textheight]{output/html_files/state.pdf}
\caption{The state branch.}
\end{figure}

\hypertarget{state}{%
\subsection{state}\label{state}}

\textbf{Elucidation:} A `physical' whose spatial direct parts extends
from one change in spatial direct part cardinality (i.e.~the number of
spatial direct parts) to the immidiate next change.

\textbf{Example:} e.g.~the existent in my glass is declared at t =
t\_start as made of two direct parts: the ice and the water. It will
continue to exists as state as long as the ice is completely melt at t =
t\_end. The new state will be completely made of water. Between t\_start
and t\_end there is an exchange of molecules between the ice and the
water, but this does not affect the existence of the two states.

If we partition the existent in my glass as ice surrounded by several
molecules (we do not use the object water as direct part) then the
appearance of a molecule coming from the ice will cause a state to end
and another state to begin.

\textbf{Comment:} Direct partitions declaration is a choice of the
ontology developer that choses the classes to be used as direct parts,
according to its own world view.

A `state' can always be direct partitioned in `elementary'-s and `void'
or `physical'.

e.g.~the water in my glass can be seen as a single object without
declaring direct parts, or as made of H2O molecules direct parts.

\textbf{Comment:} The definition of `state' implies that its direct
parts (i.e. `physicals') are not gained or lost during its temporal
extension (they exist from the left to the right side of the time
interval), so that the granularity of a `state' is constant.

This does not mean that there cannot be a change in the internal
structure of the `state' direct parts. It means only that this change
must not affect the existence of the direct part itself.

There is no change in granularity or cardinality of direct parts within
a `state'.

Also, the `state' must cover all the time interval between two
successive cardinality changes.

The use of spatial direct parthood in `state' definition means that a
`state' cannot overlap in space another `state'.

\textbf{Comment:} The usefulness of `state' is that it makes it possible
to describe the evolution in time of an `existent' in terms of series of
`state'-s that can take into account the disappearance or appearance of
parts within a `physical'.

A `state' is a recognizable granularity level of matter, in the sense
that its direct parts do not appear or disappear within its lifetime as
it can be for a generic `existent'.

\textbf{Comment:} There is no change in granularity or cardinality of
parts within a state.

The use of spatial direct parthood in state definition means that a
state cannot overlap in space another state that is direct part of the
same whole.

\textbf{IRI:}
\url{http://emmc.info/emmo-direct\#EMMO_36c79456_e29c_400d_8bd3_0eedddb82652}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{existent}{existent}
\item
  is\_a \protect\hyperlink{quantum}{quantum} or
  (\protect\hyperlink{has_spatial_direct_part}{has\_spatial\_direct\_part}
  some \protect\hyperlink{existent}{existent})
\end{itemize}

\hypertarget{elementary}{%
\subsection{elementary}\label{elementary}}

\textbf{Elucidation:} The basic constituent of `physical'-s that can be
proper partitioned only in time up to quantum level.

\textbf{Comment:} `elementary' is by definition the most simple example
of `state'.

\textbf{Comment:} According to mereology, this should be call
`a-tomistic' in the strict etimological sense of the word (from greek,
a-tomos: un-divisible).

Mereology based on such items is called atomistic mereology.

However, in order not to confuse the lexicon between mereology and
physics (in which an atom is a divisible physical entity) we prefer to
call it `elementary', recalling the concept of elementary particle
coming from the standard particles model.

\textbf{IRI:}
\url{http://emmc.info/emmo-core\#EMMO_0f795e3e_c602_4577_9a43_d5a231aa1360}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{subatomic}{subatomic}
\item
  is\_a \protect\hyperlink{state}{state}
\item
  is\_a \protect\hyperlink{quantum}{quantum} or
  (\protect\hyperlink{has_temporal_part}{has\_temporal\_part} only
  \protect\hyperlink{elementary}{elementary})
\end{itemize}

\hypertarget{massive}{%
\subsection{massive}\label{massive}}

\textbf{IRI:}
\url{http://emmc.info/emmo-material\#EMMO_385b8f6e_43ac_4596_ad76_ac322c68b7ca}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{elementary}{elementary}
\end{itemize}

\hypertarget{electron}{%
\subsection{electron}\label{electron}}

\textbf{IRI:}
\url{http://emmc.info/emmo-material\#EMMO_8043d3c6_a4c1_4089_ba34_9744e28e5b3d}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{massive}{massive}
\end{itemize}

\hypertarget{quark}{%
\subsection{quark}\label{quark}}

\textbf{IRI:}
\url{http://emmc.info/emmo-material\#EMMO_72d53756_7fb1_46ed_980f_83f47efbe105}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{massive}{massive}
\end{itemize}

\hypertarget{massless}{%
\subsection{massless}\label{massless}}

\textbf{IRI:}
\url{http://emmc.info/emmo-material\#EMMO_e5488299_8dab_4ebb_900a_26d2abed8396}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{elementary}{elementary}
\end{itemize}

\hypertarget{photon}{%
\subsection{photon}\label{photon}}

\textbf{IRI:}
\url{http://emmc.info/emmo-material\#EMMO_25f8b804_9a0b_4387_a3e7_b35bce5365ee}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{massless}{massless}
\end{itemize}

\hypertarget{gluon}{%
\subsection{gluon}\label{gluon}}

\textbf{IRI:}
\url{http://emmc.info/emmo-material\#EMMO_7db59e56_f68b_48b7_ae99_891c35ae5c3b}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{massless}{massless}
\end{itemize}

\hypertarget{graviton}{%
\subsection{graviton}\label{graviton}}

\textbf{IRI:}
\url{http://emmc.info/emmo-material\#EMMO_eb3c61f0_3983_4346_a0c6_e7f6b90a67a8}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{massless}{massless}
\end{itemize}

\hypertarget{subatomic}{%
\subsection{subatomic}\label{subatomic}}

\textbf{IRI:}
\url{http://emmc.info/emmo-material\#EMMO_7d66bde4_b68d_41cc_b5fc_6fd98c5e2ff0}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{state}{state}
\end{itemize}

\hypertarget{elementary-1}{%
\subsection{elementary}\label{elementary-1}}

\textbf{Elucidation:} The basic constituent of `physical'-s that can be
proper partitioned only in time up to quantum level.

\textbf{Comment:} `elementary' is by definition the most simple example
of `state'.

\textbf{Comment:} According to mereology, this should be call
`a-tomistic' in the strict etimological sense of the word (from greek,
a-tomos: un-divisible).

Mereology based on such items is called atomistic mereology.

However, in order not to confuse the lexicon between mereology and
physics (in which an atom is a divisible physical entity) we prefer to
call it `elementary', recalling the concept of elementary particle
coming from the standard particles model.

\textbf{IRI:}
\url{http://emmc.info/emmo-core\#EMMO_0f795e3e_c602_4577_9a43_d5a231aa1360}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{subatomic}{subatomic}
\item
  is\_a \protect\hyperlink{state}{state}
\item
  is\_a \protect\hyperlink{quantum}{quantum} or
  (\protect\hyperlink{has_temporal_part}{has\_temporal\_part} only
  \protect\hyperlink{elementary}{elementary})
\end{itemize}

\hypertarget{massive-1}{%
\subsection{massive}\label{massive-1}}

\textbf{IRI:}
\url{http://emmc.info/emmo-material\#EMMO_385b8f6e_43ac_4596_ad76_ac322c68b7ca}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{elementary}{elementary}
\end{itemize}

\hypertarget{electron-1}{%
\subsection{electron}\label{electron-1}}

\textbf{IRI:}
\url{http://emmc.info/emmo-material\#EMMO_8043d3c6_a4c1_4089_ba34_9744e28e5b3d}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{massive}{massive}
\end{itemize}

\hypertarget{quark-1}{%
\subsection{quark}\label{quark-1}}

\textbf{IRI:}
\url{http://emmc.info/emmo-material\#EMMO_72d53756_7fb1_46ed_980f_83f47efbe105}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{massive}{massive}
\end{itemize}

\hypertarget{massless-1}{%
\subsection{massless}\label{massless-1}}

\textbf{IRI:}
\url{http://emmc.info/emmo-material\#EMMO_e5488299_8dab_4ebb_900a_26d2abed8396}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{elementary}{elementary}
\end{itemize}

\hypertarget{photon-1}{%
\subsection{photon}\label{photon-1}}

\textbf{IRI:}
\url{http://emmc.info/emmo-material\#EMMO_25f8b804_9a0b_4387_a3e7_b35bce5365ee}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{massless}{massless}
\end{itemize}

\hypertarget{gluon-1}{%
\subsection{gluon}\label{gluon-1}}

\textbf{IRI:}
\url{http://emmc.info/emmo-material\#EMMO_7db59e56_f68b_48b7_ae99_891c35ae5c3b}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{massless}{massless}
\end{itemize}

\hypertarget{graviton-1}{%
\subsection{graviton}\label{graviton-1}}

\textbf{IRI:}
\url{http://emmc.info/emmo-material\#EMMO_eb3c61f0_3983_4346_a0c6_e7f6b90a67a8}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{massless}{massless}
\end{itemize}

\hypertarget{electron_cloud}{%
\subsection{electron\_cloud}\label{electron_cloud}}

\textbf{Elucidation:} A `spacetime' that stands for a quantum system
made of electrons.

\textbf{IRI:}
\url{http://emmc.info/emmo-material\#EMMO_1067b97a_84f8_4d22_8ace_b842b8ce355c}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{matter}{matter}
\item
  is\_a \protect\hyperlink{subatomic}{subatomic}
\item
  (\protect\hyperlink{has_spatial_direct_part}{has\_spatial\_direct\_part}
  some \protect\hyperlink{electron}{electron})
\end{itemize}

\hypertarget{nucleon}{%
\subsection{nucleon}\label{nucleon}}

\textbf{IRI:}
\url{http://emmc.info/emmo-material\#EMMO_50781fd9_a9e4_46ad_b7be_4500371d188d}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{matter}{matter}
\item
  is\_a \protect\hyperlink{subatomic}{subatomic}
\end{itemize}

\hypertarget{proton}{%
\subsection{proton}\label{proton}}

\textbf{IRI:}
\url{http://emmc.info/emmo-material\#EMMO_8f87e700_99a8_4427_8ffb_e493de05c217}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{nucleon}{nucleon}
\item
  (\protect\hyperlink{has_spatial_direct_part}{has\_spatial\_direct\_part}
  some \protect\hyperlink{quark}{quark})
\end{itemize}

\hypertarget{neutron}{%
\subsection{neutron}\label{neutron}}

\textbf{IRI:}
\url{http://emmc.info/emmo-material\#EMMO_df808271_df91_4f27_ba59_fa423c51896c}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{nucleon}{nucleon}
\item
  (\protect\hyperlink{has_spatial_direct_part}{has\_spatial\_direct\_part}
  some \protect\hyperlink{quark}{quark})
\end{itemize}

\hypertarget{nucleus}{%
\subsection{nucleus}\label{nucleus}}

\textbf{IRI:}
\url{http://emmc.info/emmo-material\#EMMO_f835f4d4_c665_403d_ab25_dca5cc74be52}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{matter}{matter}
\item
  is\_a \protect\hyperlink{subatomic}{subatomic}
\item
  (\protect\hyperlink{has_spatial_direct_part}{has\_spatial\_direct\_part}
  some \protect\hyperlink{nucleon}{nucleon})
\item
  (\protect\hyperlink{has_spatial_direct_part}{has\_spatial\_direct\_part}
  min 1 \protect\hyperlink{proton}{proton})
\end{itemize}

\hypertarget{mesoscopic}{%
\subsection{mesoscopic}\label{mesoscopic}}

\textbf{IRI:}
\url{http://emmc.info/emmo-material\#EMMO_174cf221_9d16_427c_abea_e217a948969b}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{state}{state}
\end{itemize}

\hypertarget{molecule}{%
\subsection{molecule}\label{molecule}}

\textbf{Elucidation:} An atom\_based state defined by an exact number of
e-bonded atomic species and an electron cloud made of the shared
electrons.

\textbf{Example:} H20, C6H12O6, CH4

\textbf{Comment:} An entity is called essential if removing one direct
part will lead to a change in entity class.

An entity is called redundand if removing one direct part will not lead
to a change in entity class.

\textbf{Comment:} This definition states that this object is a
non-periodic set of atoms or a set with a finite periodicity.

Removing an atom from the state will result in another type of
atom\_based state.

e.g.~you cannot remove H from H20 without changing the molecule type
(essential). However, you can remove a C from a nanotube (redundant).
C60 fullerene is a molecule, since it has a finite periodicity and is
made of a well defined number of atoms (essential). A C nanotube is not
a molecule, since it has an infinite periodicity (redundant).

\textbf{IRI:}
\url{http://emmc.info/emmo-material\#EMMO_3397f270_dfc1_4500_8f6f_4d0d85ac5f71}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{mesoscopic}{mesoscopic}
\item
  is\_a \protect\hyperlink{matter}{matter}
\item
  (\protect\hyperlink{has_spatial_direct_part}{has\_spatial\_direct\_part}
  min 2 \protect\hyperlink{e-bonded_atom}{e-bonded\_atom})
\item
  (\protect\hyperlink{has_spatial_direct_part}{has\_spatial\_direct\_part}
  exactly 1 \protect\hyperlink{electron_cloud}{electron\_cloud})
\end{itemize}

\hypertarget{atomic}{%
\subsection{atomic}\label{atomic}}

\textbf{IRI:}
\url{http://emmc.info/emmo-material\#EMMO_5c4aff3c_c30c_4507_86d5_b4df41eb9f2f}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{state}{state}
\end{itemize}

\hypertarget{atom}{%
\subsection{atom}\label{atom}}

\textbf{Elucidation:} An `atom' is a `nucleus' surrounded by an
`electron\_cloud', i.e.~a quantum system made of one or more bounded
electrons.

\textbf{Example:} A standalone atom has direct part one `nucleus' and
one `electron\_cloud'.

An O `atom' within an O2 `molecule' is an `e-bonded\_atom'.

In this material branch, H atom is a particular case, with respect to
higher atomic number atoms, since as soon as it shares its electron it
has no nucleus entangled electron cloud.

We cannot say that H2 molecule has direct part two H atoms, but has
direct part two H nucleus.

\textbf{IRI:}
\url{http://emmc.info/emmo-material\#EMMO_eb77076b_a104_42ac_a065_798b2d2809ad}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{matter}{matter}
\item
  is\_a \protect\hyperlink{atomic}{atomic}
\item
  (\protect\hyperlink{has_spatial_direct_part}{has\_spatial\_direct\_part}
  exactly 1 \protect\hyperlink{electron_cloud}{electron\_cloud})
\item
  (\protect\hyperlink{has_spatial_direct_part}{has\_spatial\_direct\_part}
  exactly 1 \protect\hyperlink{nucleus}{nucleus})
\end{itemize}

\hypertarget{standalone_atom}{%
\subsection{standalone\_atom}\label{standalone_atom}}

\textbf{Elucidation:} An atom that does not share electrons with other
atoms.

\textbf{Comment:} A standalone atom can be bonded with other atoms by
intermolecular forces (i.e.~dipole--dipole, London dispersion force,
hydrogen bonding), since this bonds does not involve electron sharing.

\textbf{IRI:}
\url{http://emmc.info/emmo-material\#EMMO_2fd3f574_5e93_47fe_afca_ed80b0a21ab4}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{atom}{atom}
\end{itemize}

\hypertarget{neutral_atom}{%
\subsection{neutral\_atom}\label{neutral_atom}}

\textbf{Elucidation:} A standalone atom that has no net charge.

\textbf{IRI:}
\url{http://emmc.info/emmo-material\#EMMO_4588526f_8553_4f4d_aa73_a483e88d599b}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{standalone_atom}{standalone\_atom}
\end{itemize}

\hypertarget{ion_atom}{%
\subsection{ion\_atom}\label{ion_atom}}

\textbf{Elucidation:} A standalone atom with an unbalanced number of
electrons with respect to its atomic number.

\textbf{Comment:} The ion\_atom is the basic part of a pure ionic bonded
compound i.e.~without eclectron sharing,

\textbf{IRI:}
\url{http://emmc.info/emmo-material\#EMMO_db03061b_db31_4132_a47a_6a634846578b}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{standalone_atom}{standalone\_atom}
\end{itemize}

\hypertarget{e-bonded_atom}{%
\subsection{e-bonded\_atom}\label{e-bonded_atom}}

\textbf{Elucidation:} An electronic bonded atom that shares at least one
electron to the atom\_based entity of which is part of.

\textbf{Comment:} A real bond between atoms is always something hybrid
between covalent, metallic and ionic.

In general, metallic and ionic bonds have atoms sharing electrons.

\textbf{Comment:} The bond types that are covered by this definition are
the strong electonic bonds: covalent, metallic and ionic.

\textbf{Comment:} This class can be used to represent molecules as
simplified quantum systems, in which outer molecule shared electrons are
un-entangled with the inner shells of the atoms composing the molecule.

\textbf{IRI:}
\url{http://emmc.info/emmo-material\#EMMO_8303a247_f9d9_4616_bdcd_f5cbd7b298e3}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{atom}{atom}
\end{itemize}

\hypertarget{continuum}{%
\subsection{continuum}\label{continuum}}

\textbf{Elucidation:} A state that is a collection of sufficiently large
number of other parts such that: - it is the bearer of qualities that
can exists only by the fact that it is a sum of parts - the smallest
partition dV of the state volume in which we are interested in, contains
enough parts to be statistically consistent: n {[}\#/m3{]} x dV {[}m3{]}
\textgreater{}\textgreater{} 1

\textbf{Comment:} A continuum is made of a sufficient number of parts
that it continues to exists as continuum individual even after the loss
of one of them i.e.~a continuum is a redundant.

\textbf{Comment:} A continuum is not necessarily small (i.e.~composed by
the minimum amount of sates to fulfill the definition).

A single continuum individual can be the whole fluid in a pipe.

\textbf{Comment:} A continuum is the bearer of properties that are
generated by the interactions of parts such as viscosity and thermal or
electrical conductivity.

\textbf{IRI:}
\url{http://emmc.info/emmo-material\#EMMO_8b0923ab_b500_477b_9ce9_8b3a3e4dc4f2}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{state}{state}
\end{itemize}

\hypertarget{fluid}{%
\subsection{fluid}\label{fluid}}

\textbf{Elucidation:} A continuum that has no fixed shape and yields
easily to external pressure.

\textbf{Example:} Gas, liquid, plasma,

\textbf{IRI:}
\url{http://emmc.info/emmo-material\#EMMO_87ac88ff_8379_4f5a_8c7b_424a8fff1ee8}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{continuum}{continuum}
\end{itemize}

\hypertarget{solid}{%
\subsection{solid}\label{solid}}

\textbf{Elucidation:} A continuum characterized by structural rigidity
and resistance to changes of shape or volume, that retains its shape and
density when not confined.

\textbf{IRI:}
\url{http://emmc.info/emmo-material\#EMMO_a2b006f2_bbfd_4dba_bcaa_3fca20cd6be1}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{continuum}{continuum}
\end{itemize}

\hypertarget{matter-branch}{%
\section{matter branch}\label{matter-branch}}

\begin{figure}
\centering
\includegraphics[width=5.88542in,height=\textheight]{output/html_files/matter.pdf}
\caption{The matter branch.}
\end{figure}

\hypertarget{matter}{%
\subsection{matter}\label{matter}}

\textbf{Elucidation:} A `physical' that possesses some `massive' parts.

\textbf{IRI:}
\url{http://emmc.info/emmo-material\#EMMO_5b2222df_4da6_442f_8244_96e9e45887d1}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{physical}{physical}
\item
  equivalent\_to (\protect\hyperlink{has_part}{has\_part} some
  \protect\hyperlink{massive}{massive})
\end{itemize}

\hypertarget{electron_cloud-1}{%
\subsection{electron\_cloud}\label{electron_cloud-1}}

\textbf{Elucidation:} A `spacetime' that stands for a quantum system
made of electrons.

\textbf{IRI:}
\url{http://emmc.info/emmo-material\#EMMO_1067b97a_84f8_4d22_8ace_b842b8ce355c}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{matter}{matter}
\item
  is\_a \protect\hyperlink{subatomic}{subatomic}
\item
  (\protect\hyperlink{has_spatial_direct_part}{has\_spatial\_direct\_part}
  some \protect\hyperlink{electron}{electron})
\end{itemize}

\hypertarget{atom-1}{%
\subsection{atom}\label{atom-1}}

\textbf{Elucidation:} An `atom' is a `nucleus' surrounded by an
`electron\_cloud', i.e.~a quantum system made of one or more bounded
electrons.

\textbf{Example:} A standalone atom has direct part one `nucleus' and
one `electron\_cloud'.

An O `atom' within an O2 `molecule' is an `e-bonded\_atom'.

In this material branch, H atom is a particular case, with respect to
higher atomic number atoms, since as soon as it shares its electron it
has no nucleus entangled electron cloud.

We cannot say that H2 molecule has direct part two H atoms, but has
direct part two H nucleus.

\textbf{IRI:}
\url{http://emmc.info/emmo-material\#EMMO_eb77076b_a104_42ac_a065_798b2d2809ad}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{matter}{matter}
\item
  is\_a \protect\hyperlink{atomic}{atomic}
\item
  (\protect\hyperlink{has_spatial_direct_part}{has\_spatial\_direct\_part}
  exactly 1 \protect\hyperlink{electron_cloud}{electron\_cloud})
\item
  (\protect\hyperlink{has_spatial_direct_part}{has\_spatial\_direct\_part}
  exactly 1 \protect\hyperlink{nucleus}{nucleus})
\end{itemize}

\hypertarget{standalone_atom-1}{%
\subsection{standalone\_atom}\label{standalone_atom-1}}

\textbf{Elucidation:} An atom that does not share electrons with other
atoms.

\textbf{Comment:} A standalone atom can be bonded with other atoms by
intermolecular forces (i.e.~dipole--dipole, London dispersion force,
hydrogen bonding), since this bonds does not involve electron sharing.

\textbf{IRI:}
\url{http://emmc.info/emmo-material\#EMMO_2fd3f574_5e93_47fe_afca_ed80b0a21ab4}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{atom}{atom}
\end{itemize}

\hypertarget{neutral_atom-1}{%
\subsection{neutral\_atom}\label{neutral_atom-1}}

\textbf{Elucidation:} A standalone atom that has no net charge.

\textbf{IRI:}
\url{http://emmc.info/emmo-material\#EMMO_4588526f_8553_4f4d_aa73_a483e88d599b}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{standalone_atom}{standalone\_atom}
\end{itemize}

\hypertarget{ion_atom-1}{%
\subsection{ion\_atom}\label{ion_atom-1}}

\textbf{Elucidation:} A standalone atom with an unbalanced number of
electrons with respect to its atomic number.

\textbf{Comment:} The ion\_atom is the basic part of a pure ionic bonded
compound i.e.~without eclectron sharing,

\textbf{IRI:}
\url{http://emmc.info/emmo-material\#EMMO_db03061b_db31_4132_a47a_6a634846578b}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{standalone_atom}{standalone\_atom}
\end{itemize}

\hypertarget{e-bonded_atom-1}{%
\subsection{e-bonded\_atom}\label{e-bonded_atom-1}}

\textbf{Elucidation:} An electronic bonded atom that shares at least one
electron to the atom\_based entity of which is part of.

\textbf{Comment:} A real bond between atoms is always something hybrid
between covalent, metallic and ionic.

In general, metallic and ionic bonds have atoms sharing electrons.

\textbf{Comment:} The bond types that are covered by this definition are
the strong electonic bonds: covalent, metallic and ionic.

\textbf{Comment:} This class can be used to represent molecules as
simplified quantum systems, in which outer molecule shared electrons are
un-entangled with the inner shells of the atoms composing the molecule.

\textbf{IRI:}
\url{http://emmc.info/emmo-material\#EMMO_8303a247_f9d9_4616_bdcd_f5cbd7b298e3}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{atom}{atom}
\end{itemize}

\hypertarget{molecule-1}{%
\subsection{molecule}\label{molecule-1}}

\textbf{Elucidation:} An atom\_based state defined by an exact number of
e-bonded atomic species and an electron cloud made of the shared
electrons.

\textbf{Example:} H20, C6H12O6, CH4

\textbf{Comment:} An entity is called essential if removing one direct
part will lead to a change in entity class.

An entity is called redundand if removing one direct part will not lead
to a change in entity class.

\textbf{Comment:} This definition states that this object is a
non-periodic set of atoms or a set with a finite periodicity.

Removing an atom from the state will result in another type of
atom\_based state.

e.g.~you cannot remove H from H20 without changing the molecule type
(essential). However, you can remove a C from a nanotube (redundant).
C60 fullerene is a molecule, since it has a finite periodicity and is
made of a well defined number of atoms (essential). A C nanotube is not
a molecule, since it has an infinite periodicity (redundant).

\textbf{IRI:}
\url{http://emmc.info/emmo-material\#EMMO_3397f270_dfc1_4500_8f6f_4d0d85ac5f71}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{mesoscopic}{mesoscopic}
\item
  is\_a \protect\hyperlink{matter}{matter}
\item
  (\protect\hyperlink{has_spatial_direct_part}{has\_spatial\_direct\_part}
  min 2 \protect\hyperlink{e-bonded_atom}{e-bonded\_atom})
\item
  (\protect\hyperlink{has_spatial_direct_part}{has\_spatial\_direct\_part}
  exactly 1 \protect\hyperlink{electron_cloud}{electron\_cloud})
\end{itemize}

\hypertarget{nucleon-1}{%
\subsection{nucleon}\label{nucleon-1}}

\textbf{IRI:}
\url{http://emmc.info/emmo-material\#EMMO_50781fd9_a9e4_46ad_b7be_4500371d188d}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{matter}{matter}
\item
  is\_a \protect\hyperlink{subatomic}{subatomic}
\end{itemize}

\hypertarget{proton-1}{%
\subsection{proton}\label{proton-1}}

\textbf{IRI:}
\url{http://emmc.info/emmo-material\#EMMO_8f87e700_99a8_4427_8ffb_e493de05c217}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{nucleon}{nucleon}
\item
  (\protect\hyperlink{has_spatial_direct_part}{has\_spatial\_direct\_part}
  some \protect\hyperlink{quark}{quark})
\end{itemize}

\hypertarget{neutron-1}{%
\subsection{neutron}\label{neutron-1}}

\textbf{IRI:}
\url{http://emmc.info/emmo-material\#EMMO_df808271_df91_4f27_ba59_fa423c51896c}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{nucleon}{nucleon}
\item
  (\protect\hyperlink{has_spatial_direct_part}{has\_spatial\_direct\_part}
  some \protect\hyperlink{quark}{quark})
\end{itemize}

\hypertarget{nucleus-1}{%
\subsection{nucleus}\label{nucleus-1}}

\textbf{IRI:}
\url{http://emmc.info/emmo-material\#EMMO_f835f4d4_c665_403d_ab25_dca5cc74be52}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{matter}{matter}
\item
  is\_a \protect\hyperlink{subatomic}{subatomic}
\item
  (\protect\hyperlink{has_spatial_direct_part}{has\_spatial\_direct\_part}
  some \protect\hyperlink{nucleon}{nucleon})
\item
  (\protect\hyperlink{has_spatial_direct_part}{has\_spatial\_direct\_part}
  min 1 \protect\hyperlink{proton}{proton})
\end{itemize}

\hypertarget{sign-branch}{%
\section{sign branch}\label{sign-branch}}

\begin{figure}
\centering
\includegraphics[width=6.95833in,height=\textheight]{output/html_files/sign.pdf}
\caption{The sign branch.}
\end{figure}

\hypertarget{sign}{%
\subsection{sign}\label{sign}}

\textbf{Elucidation:} An `spacetime' that is used as sign (``semeion''
in greek) that stands for another `spacetime' through an semiotic
process.

\textbf{Example:} A novel is made of chapters, paragraphs, sentences,
words and characters (in a direct parthood mereological hierarchy).

Each of them are `sign'-s.

A character can be the a-tomistic `sign' for the class of texts.

The horizontal segment in the character ``A'' is direct part of ``A''
but it is not a `sign' itself.

For plain text we can propose the ASCII symbols, for math the
fundamental math symbols.

\textbf{Comment:} A `sign' can have temporal-direct-parts which are
`sign' themselves.

A `sign' usually have `sign' spatial direct parts only up to a certain
elementary semiotic level, in which the part is only a `physical' and no
more a `sign' (i.e.~it stands for nothing). This elementary semiotic
level is peculiar to each particular system of signs (e.g.~text,
painting).

Just like an `elementary' in the `physical' branch, each `sign' branch
should have an a-tomistic mereological part.

\textbf{Comment:} According to Peirce, `sign' includes three
subcategories: - symbols: that stand for an object through convention -
indeces: that stand for an object due to causal continguity - icon: that
stand for an object due to similitudes e.g.~in shape or composition

\textbf{Comment:} In a 4D ontology one could question if a `sign' should
be defined as a spatial direct part of a `semiosis' i.e.~a proper part
of a `semiosis' during all its existence.

e.g.~one can say that an unread text is not a `sign': it was a `sign'
during the `semiosis' process in which it was written, but after that it
is something else, until somebody read it again.

However, this is not the case for an ontology, since declaring an
individual under the `sign' class (a semiosis outside the EMMO, a
meta-semiosis) is equivalent to say that for the ontologist (an
interpreter outside the EMMO, a meta-interpreter) the real entity (an
object outside the EMMO, a meta-object) is a `sign'.

So the `semiosis' process within the EMMO is about how other
`interpreter'-s deal with the `sign'-s here declared.

\textbf{Comment:} It can be defined as the semiotic branch of the EMMO.

`sign' subclasses categorize the type of signs that are used to create
representations/models of the real world entities.

\textbf{IRI:}
\url{http://emmc.info/emmo-semiotics\#EMMO_b21a56ed_f969_4612_a6ec_cb7766f7f31d}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{semiotic}{semiotic}
\item
  (\protect\hyperlink{has_temporal_part}{has\_temporal\_part} only
  \protect\hyperlink{sign}{sign})
\item
  equivalent\_to \protect\hyperlink{index}{index} or
  \protect\hyperlink{conventional}{conventional} or
  \protect\hyperlink{icon}{icon}
\end{itemize}

\hypertarget{index}{%
\subsection{index}\label{index}}

\textbf{Elucidation:} A `sign' that stands for an 'objectì due to causal
continguity.

\textbf{Example:} Smoke stands for a combustion process (a fire).

My facial expression stands for my emotional status.

\textbf{IRI:}
\url{http://emmc.info/emmo-semiotics\#EMMO_0cd58641_824c_4851_907f_f4c3be76630c}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{sign}{sign}
\end{itemize}

\hypertarget{icon}{%
\subsection{icon}\label{icon}}

\textbf{Elucidation:} A `sign' that stands for an `object' by resembling
or imitating it, in shape or by sharing a similar logical structure.

\textbf{Example:} A picture that reproduces the aspect of a person.

An equation that reproduces the logical connection of the properties of
a physical entity.

\textbf{Comment:} Three subtypes of icon are possible:

\begin{enumerate}
\def\labelenumi{(\alph{enumi})}
\item
  the image, which depends on a simple quality (e.g.~picture)
\item
  the diagram, whose internal relations, mainly dyadic or so taken,
  represent by analogy the relations in something (e.g.~math formula,
  geometric flowchart)
\item
  the metaphor, which represents the representative character of a sign
  by representing a parallelism in something else
\end{enumerate}

{[}Wikipedia{]}

\textbf{IRI:}
\url{http://emmc.info/emmo-semiotics\#EMMO_d7788d1a_020d_4c78_85a1_13563fcec168}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{sign}{sign}
\end{itemize}

\hypertarget{model}{%
\subsection{model}\label{model}}

\textbf{Elucidation:} A `sign' that not only stands for a `physical' or
a `process', but it is also a simplified representation, aimed to assist
calculations for its description or for predictions of its behaviour.

A `model' represents a `physical' or a `process' by direct similitude
(e.g.~small scale replica) or by capturing in a logical framework the
relations between its properties (e.g.~mathematical model).

\textbf{Comment:} A `model' prediction is always a prediction of the
properties of an entity, since an entity is known by an interpreter only
through perception.

\textbf{IRI:}
\url{http://emmc.info/emmo-models\#EMMO_939483b1_0148_43d1_8b35_851d2cd5d939}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{icon}{icon}
\item
  equivalent\_to (Inverse(emmo-models.has\_model) some
  \protect\hyperlink{physical}{physical})
\end{itemize}

\hypertarget{mathematical_model}{%
\subsection{mathematical\_model}\label{mathematical_model}}

\textbf{IRI:}
\url{http://emmc.info/emmo-models\#EMMO_f7ed665b_c2e1_42bc_889b_6b42ed3a36f0}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{mathematical}{mathematical}
\item
  is\_a \protect\hyperlink{model}{model}
\end{itemize}

\hypertarget{physics_based_model}{%
\subsection{physics\_based\_model}\label{physics_based_model}}

\textbf{Elucidation:} A solvable set of one Physics Equation and one or
more Materials Relations.

\textbf{IRI:}
\url{http://emmc.info/emmo-models\#EMMO_b29fd350_39aa_4af7_9459_3faa0544cba6}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{mathematical_model}{mathematical\_model}
\item
  (\protect\hyperlink{has_spatial_part}{has\_spatial\_part} some
  \protect\hyperlink{physics_equation}{physics\_equation})
\item
  (\protect\hyperlink{has_spatial_part}{has\_spatial\_part} some
  \protect\hyperlink{material_relation}{material\_relation})
\end{itemize}

\hypertarget{continuum_model}{%
\subsection{continuum\_model}\label{continuum_model}}

\textbf{IRI:}
\url{http://emmc.info/emmo-models\#EMMO_4456a5d2_16a6_4ee1_9a8e_5c75956b28ea}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{physics_based_model}{physics\_based\_model}
\end{itemize}

\hypertarget{mesoscopic_model}{%
\subsection{mesoscopic\_model}\label{mesoscopic_model}}

\textbf{IRI:}
\url{http://emmc.info/emmo-models\#EMMO_53935db0_af45_4426_b9e9_244a0d77db00}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{physics_based_model}{physics\_based\_model}
\end{itemize}

\hypertarget{electronic_model}{%
\subsection{electronic\_model}\label{electronic_model}}

\textbf{IRI:}
\url{http://emmc.info/emmo-models\#EMMO_6eca09be_17e9_445e_abc9_000aa61b7a11}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{physics_based_model}{physics\_based\_model}
\end{itemize}

\hypertarget{atomistic_model}{%
\subsection{atomistic\_model}\label{atomistic_model}}

\textbf{IRI:}
\url{http://emmc.info/emmo-models\#EMMO_84cadc45_6758_46f2_ba2a_5ead65c70213}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{physics_based_model}{physics\_based\_model}
\end{itemize}

\hypertarget{data_based_model}{%
\subsection{data\_based\_model}\label{data_based_model}}

\textbf{Elucidation:} A computational model that uses data to create new
insight into the behaviour of a system.

\textbf{IRI:}
\url{http://emmc.info/emmo-models\#EMMO_a4b14b83_9392_4a5f_a2e8_b2b58793f59b}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{mathematical_model}{mathematical\_model}
\end{itemize}

\hypertarget{conventional}{%
\subsection{conventional}\label{conventional}}

\textbf{Elucidation:} A `sign' that stand for an `object' through
convention, norm or habit, without any resemblance to it.

\textbf{Comment:} In Peirce semiotics this kind of sign category is
called symbol. However, since symbol is also used in formal languages,
the name is changed in conventional.

\textbf{IRI:}
\url{http://emmc.info/emmo-semiotics\#EMMO_35d2e130_6e01_41ed_94f7_00b333d46cf9}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{sign}{sign}
\end{itemize}

\hypertarget{theory}{%
\subsection{theory}\label{theory}}

\textbf{Elucidation:} A `conventional' that stand for a `physical'.

\textbf{Comment:} The `theory' is e.g.~a proposition, a book or a paper
whose sub-symbols suggest in the mind of the interpreter an interpretant
structure that can represent a `physical'.

It is not an `icon' (like a math equation), because it has no common
resemblance or logical structure with the `physical'.

In Peirce semiotics: legisign-symbol-argument

\textbf{IRI:}
\url{http://emmc.info/emmo-models\#EMMO_8d2d9374_ef3a_47e6_8595_6bc208e07519}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{conventional}{conventional}
\end{itemize}

\hypertarget{natural_law}{%
\subsection{natural\_law}\label{natural_law}}

\textbf{IRI:}
\url{http://emmc.info/emmo-models\#EMMO_db9a009e_f097_43f5_9520_6cbc07e7610b}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{theory}{theory}
\end{itemize}

\hypertarget{physical_law}{%
\subsection{physical\_law}\label{physical_law}}

\textbf{IRI:}
\url{http://emmc.info/emmo-models\#EMMO_9c32fd69_f480_4130_83b3_fb25d9face14}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{natural_law}{natural\_law}
\end{itemize}

\hypertarget{material_law}{%
\subsection{material\_law}\label{material_law}}

\textbf{IRI:}
\url{http://emmc.info/emmo-models\#EMMO_f19ff3b4_6bfe_4c41_a2b2_9affd39c140b}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{natural_law}{natural\_law}
\end{itemize}

\hypertarget{interpretant}{%
\subsection{interpretant}\label{interpretant}}

\textbf{IRI:}
\url{http://emmc.info/emmo-semiotics\#EMMO_054af807_85cd_4a13_8eba_119dfdaaf38b}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{sign}{sign}
\end{itemize}

\hypertarget{symbolic-branch}{%
\section{symbolic branch}\label{symbolic-branch}}

\begin{figure}
\centering
\includegraphics[width=2.03125in,height=\textheight]{output/html_files/symbolic.pdf}
\caption{The symbolic branch.}
\end{figure}

\hypertarget{symbolic}{%
\subsection{symbolic}\label{symbolic}}

\textbf{Elucidation:} A `symbol' or a composition of `symbol'-s.

\textbf{Example:} fe@è0 emmo !5*a cat

\textbf{Comment:} In formal languages it is called a string of symbols.

\textbf{IRI:}
\url{http://emmc.info/emmo-semiotics\#EMMO_057e7d57_aff0_49de_911a_8861d85cef40}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{physical}{physical}
\item
  is\_a \protect\hyperlink{symbol}{symbol} or
  (\protect\hyperlink{has_spatial_part}{has\_spatial\_part} some
  \protect\hyperlink{symbol}{symbol})
\end{itemize}

\hypertarget{symbol-branch}{%
\section{symbol branch}\label{symbol-branch}}

\begin{figure}
\centering
\includegraphics[width=4.73958in,height=\textheight]{output/html_files/symbol.pdf}
\caption{The symbol branch.}
\end{figure}

\hypertarget{symbol}{%
\subsection{symbol}\label{symbol}}

\textbf{Elucidation:} The class of individuals that stand for an
elementary mark of a specific symbolic code (alphabet).

\textbf{Example:} The class of letter ``A'' is the symbol as idea and
the letter A is the mark.

\textbf{Comment:} Subclasses of `symbol' are alphabets, in formal
languages terminology.

\textbf{Comment:} Symbols of a formal language need not be symbols of
anything. For instance there are logical constants which do not refer to
any idea, but rather serve as a form of punctuation in the language
(e.g.~parentheses).

Symbols of a formal language must be capable of being specified without
any reference to any interpretation of them. (Wikipedia)

\textbf{Comment:} The class is the idea of the symbol, while the
individual of that class stands for a specific mark (or token) of that
idea.

\textbf{IRI:}
\url{http://emmc.info/emmo-semiotics\#EMMO_a1083d0a_c1fb_471f_8e20_a98f881ad527}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{symbolic}{symbolic}
\end{itemize}

\hypertarget{math_symbol}{%
\subsection{math\_symbol}\label{math_symbol}}

\textbf{Elucidation:} A `symbol' that is part of standard mathematical
formalism.

\textbf{IRI:}
\url{http://emmc.info/emmo-math\#EMMO_031d61af_6405_41de_8880_df2f85a53383}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{symbol}{symbol}
\item
  (\protect\hyperlink{has_spatial_part}{has\_spatial\_part} only not
  \protect\hyperlink{mathematical}{mathematical})
\end{itemize}

\hypertarget{number}{%
\subsection{number}\label{number}}

\textbf{IRI:}
\url{http://emmc.info/emmo-math\#EMMO_1a663927_3b68_4618_acd3_a8aa0d406329}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{math_symbol}{math\_symbol}
\end{itemize}

\hypertarget{variable}{%
\subsection{variable}\label{variable}}

\textbf{Comment:} A `variable' is a `symbol' that stands for a numerical
defined `mathematical' entity like e.g.~a number, a vector, a matrix.

\textbf{IRI:}
\url{http://emmc.info/emmo-math\#EMMO_1eed0732_e3f1_4b2c_a9c4_b4e75eeb5895}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{math_symbol}{math\_symbol}
\end{itemize}

\hypertarget{constant}{%
\subsection{constant}\label{constant}}

\textbf{Elucidation:} A `varaible' that stand for a well known constant.

\textbf{Comment:} pi = 3.14

\textbf{IRI:}
\url{http://emmc.info/emmo-math\#EMMO_ae15fb4f_8e4d_41de_a0f9_3997f89ba6a2}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{variable}{variable}
\end{itemize}

\hypertarget{parameter}{%
\subsection{parameter}\label{parameter}}

\textbf{Example:} Viscosity, the total energy of the system given by an
Hamiltonian, the force between two atoms.

\textbf{Comment:} A `variable' whose value is assumed to be known
independently from the equation, but whose value is not explicitated in
the equation.

\textbf{IRI:}
\url{http://emmc.info/emmo-math\#EMMO_d1d436e7_72fc_49cd_863b_7bfb4ba5276a}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{variable}{variable}
\end{itemize}

\hypertarget{unknown}{%
\subsection{unknown}\label{unknown}}

\textbf{Elucidation:} The dependent variable for which an equation has
been written.

\textbf{Example:} Velocity, for the Navier-Stokes equation.

\textbf{IRI:}
\url{http://emmc.info/emmo-math\#EMMO_fe7e56ce_118b_4243_9aad_20eb9f4f31f6}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{variable}{variable}
\end{itemize}

\hypertarget{formula-branch}{%
\section{formula branch}\label{formula-branch}}

\begin{figure}
\centering
\includegraphics[width=2.84375in,height=\textheight]{output/html_files/formula.pdf}
\caption{The formula branch.}
\end{figure}

\hypertarget{formula}{%
\subsection{formula}\label{formula}}

\textbf{Elucidation:} A composition of `symbol'-s respecting a specific
language syntactic rules (well-formed formula).

\textbf{Example:} The word ``cat'' considered as a collection of
`symbol'-s respecting the rules of english language.

In this example the `symbolic' entity ``cat'' is not related to the real
cat, but it is only a word (like it would be to an italian person that
ignores the meaning of this english word).

If an `interpreter' skilled in english language is involved in a
`semiotic' process with this word, that ``cat'' became also a `sign'
i.e.~it became for the `interpreter' a representation for a real cat.

\textbf{Comment:} In formal languages the terms word or well-formed
formula are used with the same meaning.

\textbf{IRI:}
\url{http://emmc.info/emmo-semiotics\#EMMO_50ea1ec5_f157_41b0_b46b_a9032f17ca10}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{symbolic}{symbolic}
\end{itemize}

\hypertarget{mathematical-branch}{%
\section{mathematical branch}\label{mathematical-branch}}

\begin{figure}
\centering
\includegraphics[width=6.95833in,height=\textheight]{output/html_files/mathematical.pdf}
\caption{The mathematical branch.}
\end{figure}

\hypertarget{mathematical}{%
\subsection{mathematical}\label{mathematical}}

\textbf{Comment:} The class of general mathematical symbols.

\textbf{IRI:}
\url{http://emmc.info/emmo-math\#EMMO_54ee6b5e_5261_44a8_86eb_5717e7fdb9d0}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{formula}{formula}
\end{itemize}

\hypertarget{equation}{%
\subsection{equation}\label{equation}}

\textbf{Comment:} The class of `mathematical'-s that stand for a
mathematical expression that puts in relation some variables and that
can always be represented as:

f(v0, v1, \ldots{}, vn) = g(v0, v1, \ldots{}, vn)

where f is the left hand and g the right hand side expressions and v0,
v1, \ldots{}, vn are the variables.

e.g.

x\^{}2 +3x = 5x

dv/dt = a

sin(x) = y

\textbf{IRI:}
\url{http://emmc.info/emmo-math\#EMMO_e56ee3eb_7609_4ae1_8bed_51974f0960a6}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{mathematical}{mathematical}
\item
  (\protect\hyperlink{has_spatial_part}{has\_spatial\_part} some
  \protect\hyperlink{variable}{variable})
\end{itemize}

\hypertarget{physics_equation}{%
\subsection{physics\_equation}\label{physics_equation}}

\textbf{Elucidation:} An `equation' that stands for a `physical\_law' by
mathematically defining the relations between physics\_quantities.

\textbf{Comment:} The Newton's equation of motion.

The Schrodinger equation.

The Navier-Stokes equation.

\textbf{IRI:}
\url{http://emmc.info/emmo-models\#EMMO_27c5d8c6_8af7_4d63_beb1_ec37cd8b3fa3}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{equation}{equation}
\item
  (\protect\hyperlink{has_spatial_part}{has\_spatial\_part} some
  \protect\hyperlink{physical_quantity}{physical\_quantity})
\end{itemize}

\hypertarget{material_relation}{%
\subsection{material\_relation}\label{material_relation}}

\textbf{Elucidation:} An `equation' that stands for a physical
assumption specific to a material, and provides an expression for a
`physics\_quantity' (the dependent variable) as function of other
variables, physics\_quantity or data (independent variables).

\textbf{Example:} The Lennard-Jones potential.

A force field.

An Hamiltonian.

\textbf{Comment:} A material\_relation can e.g.~return a predefined
number, return a database query, be an equation that depends on other
physics\_quantities.

\textbf{IRI:}
\url{http://emmc.info/emmo-models\#EMMO_e5438930_04e7_4d42_ade5_3700d4a52ab7}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{equation}{equation}
\item
  (\protect\hyperlink{has_spatial_part}{has\_spatial\_part} some
  \protect\hyperlink{physical_quantity}{physical\_quantity})
\end{itemize}

\hypertarget{mathematical_model-1}{%
\subsection{mathematical\_model}\label{mathematical_model-1}}

\textbf{IRI:}
\url{http://emmc.info/emmo-models\#EMMO_f7ed665b_c2e1_42bc_889b_6b42ed3a36f0}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{mathematical}{mathematical}
\item
  is\_a \protect\hyperlink{model}{model}
\end{itemize}

\hypertarget{physics_based_model-1}{%
\subsection{physics\_based\_model}\label{physics_based_model-1}}

\textbf{Elucidation:} A solvable set of one Physics Equation and one or
more Materials Relations.

\textbf{IRI:}
\url{http://emmc.info/emmo-models\#EMMO_b29fd350_39aa_4af7_9459_3faa0544cba6}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{mathematical_model}{mathematical\_model}
\item
  (\protect\hyperlink{has_spatial_part}{has\_spatial\_part} some
  \protect\hyperlink{physics_equation}{physics\_equation})
\item
  (\protect\hyperlink{has_spatial_part}{has\_spatial\_part} some
  \protect\hyperlink{material_relation}{material\_relation})
\end{itemize}

\hypertarget{continuum_model-1}{%
\subsection{continuum\_model}\label{continuum_model-1}}

\textbf{IRI:}
\url{http://emmc.info/emmo-models\#EMMO_4456a5d2_16a6_4ee1_9a8e_5c75956b28ea}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{physics_based_model}{physics\_based\_model}
\end{itemize}

\hypertarget{mesoscopic_model-1}{%
\subsection{mesoscopic\_model}\label{mesoscopic_model-1}}

\textbf{IRI:}
\url{http://emmc.info/emmo-models\#EMMO_53935db0_af45_4426_b9e9_244a0d77db00}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{physics_based_model}{physics\_based\_model}
\end{itemize}

\hypertarget{electronic_model-1}{%
\subsection{electronic\_model}\label{electronic_model-1}}

\textbf{IRI:}
\url{http://emmc.info/emmo-models\#EMMO_6eca09be_17e9_445e_abc9_000aa61b7a11}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{physics_based_model}{physics\_based\_model}
\end{itemize}

\hypertarget{atomistic_model-1}{%
\subsection{atomistic\_model}\label{atomistic_model-1}}

\textbf{IRI:}
\url{http://emmc.info/emmo-models\#EMMO_84cadc45_6758_46f2_ba2a_5ead65c70213}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{physics_based_model}{physics\_based\_model}
\end{itemize}

\hypertarget{data_based_model-1}{%
\subsection{data\_based\_model}\label{data_based_model-1}}

\textbf{Elucidation:} A computational model that uses data to create new
insight into the behaviour of a system.

\textbf{IRI:}
\url{http://emmc.info/emmo-models\#EMMO_a4b14b83_9392_4a5f_a2e8_b2b58793f59b}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{mathematical_model}{mathematical\_model}
\end{itemize}

\hypertarget{quantitative_property-branch}{%
\section{quantitative\_property
branch}\label{quantitative_property-branch}}

\begin{figure}
\centering
\includegraphics[width=3.75in,height=\textheight]{output/html_files/quantitative_property.pdf}
\caption{The quantitative\_property branch.}
\end{figure}

\hypertarget{quantitative_property}{%
\subsection{quantitative\_property}\label{quantitative_property}}

\textbf{Elucidation:} A `property' that can be quantified with respect
to a standardized reference physical instance (e.g.~the prototype meter
bar, the kg prototype) or method (e.g.~resilience) through a measurement
process.

\textbf{IRI:}
\url{http://emmc.info/emmo-physical-properties\#EMMO_dd4a7f3e_ef56_466c_ac1a_d2716b5f87ec}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{objective_property}{objective\_property}
\item
  is\_a \protect\hyperlink{formula}{formula}
\end{itemize}

\hypertarget{physical_quantity}{%
\subsection{physical\_quantity}\label{physical_quantity}}

\textbf{Elucidation:} A ``symbolic'' entity that is made of a `number'
and a `measurement\_unit'.

By definition it also stands for the result of a measurement process,
and so it is also a `sign'.

\textbf{Comment:} Measured or simulated `physical propertiy'-s are
always defined by a physical law, connected to a physical entity through
a model perspective and measurement is done according to the same model.

Systems of units suggests that this is the correct approach, since
except for the fundamental units (length, time, charge) every other unit
is derived by mathematical relations between these fundamental units,
implying a physical laws or definitions.

\textbf{IRI:}
\url{http://emmc.info/emmo-physical-properties\#EMMO_02c0621e_a527_4790_8a0f_2bb51973c819}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a
  \protect\hyperlink{quantitative_property}{quantitative\_property}
\item
  (\protect\hyperlink{has_spatial_part}{has\_spatial\_part} some
  \protect\hyperlink{number}{number})
\item
  (\protect\hyperlink{has_spatial_part}{has\_spatial\_part} some
  \protect\hyperlink{measurement_unit}{measurement\_unit})
\end{itemize}

\hypertarget{measurement_unit}{%
\subsection{measurement\_unit}\label{measurement_unit}}

\textbf{Elucidation:} A `quantitative\_property' that stands for the
standard reference magnitude of a specific class of measurement
processes, defined and adopted by convention or by law.

Quantitative measurement results are expressed as a multiple of the
`measurement\_unit'.

\textbf{IRI:}
\url{http://emmc.info/emmo-physical-properties\#EMMO_b081b346_7279_46ef_9a3d_2c088fcd79f4}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a
  \protect\hyperlink{quantitative_property}{quantitative\_property}
\end{itemize}

\hypertarget{descriptive_property}{%
\subsection{descriptive\_property}\label{descriptive_property}}

\textbf{IRI:}
\url{http://emmc.info/emmo-physical-properties\#EMMO_c46f091c_0420_4c1a_af30_0a2c8ebcf7d7}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a
  \protect\hyperlink{quantitative_property}{quantitative\_property}
\end{itemize}

\hypertarget{property-branch}{%
\section{property branch}\label{property-branch}}

\begin{figure}
\centering
\includegraphics[width=4.89583in,height=\textheight]{output/html_files/property.pdf}
\caption{The property branch.}
\end{figure}

\hypertarget{property}{%
\subsection{property}\label{property}}

\textbf{Elucidation:} A `sign' that stands for an `object' that the
`interpreter' perceived through a well defined `observation' process.

(a property is always a partial representation of an `object' since it
reflects the `object' capability to be part of a specific `observation'
process)

\textbf{Example:} Hardness is a subclass of properties.

Vickers hardness is a subclass of hardness that involves the procedures
and instruments defined by the standard hardness test.

\textbf{Example:} Let's define the class `colour' as the subclass of the
properties that involve photon emission and an electromagnetic radiation
sensible observer.

An individual C of this class `colour' can be defined be declaring the
process individual (e.g.~daylight illumination) and the observer
(e.g.~my eyes)

Stating that an entity E has\_property C, we mean that it can be
observed by such setup of process + observer (i.e.~observed by my eyes
under daylight).

This definition can be generalized by using a generic human eye, so that
the observer can be a generic human.

This can be used in material characterization, to define exactly the
type of measurement done, including the instrument type.

\textbf{Comment:} We know real world entities through
observation/perception.

A non-perceivable real world entity does not exist (or it exists on a
plane of existance that has no intersection with us and we can say
nothing about it).

Perception/observation of a real wolrd entity occurs when the entity
stimulate an observer in a peculiar way through a well defined
perception channel.

For this reason each property is related to a specific observation
process which involves a specific observer with its own perception
mechanisms.

The observation process (e.g.~a look, a photo shot, a measurement) is
performed by an observer (e.g.~you, a camera, an instrument) through a
specific perception mechanism (e.g.~retina impression, CMOS excitation,
piezoelectric sensor activation) and involves an observed entity.

An observation is a semiotic process, since it stimulate an interpretant
within the interpreter who can communicate the perception result to
other interpreters through a sign which is the property.

Property subclasses are specializations that depend on the type of
observation processes.

e.g.~the property `colour' is related to a process that involves
emission or interaction of photon and an observer who can perceive
electromagnetic radiation in the visible frequency range.

Properties usually relies on symbolic systems (e.g.~for colour it can be
palette or RGB).

\textbf{IRI:}
\url{http://emmc.info/emmo-properties\#EMMO_b7bcff25_ffc3_474e_9ab5_01b1664bd4ba}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{symbolic}{symbolic}
\item
  is\_a \protect\hyperlink{conventional}{conventional}
\item
  (Inverse(emmo-properties.has\_property) some
  \protect\hyperlink{emmo}{emmo})
\end{itemize}

\hypertarget{objective_property}{%
\subsection{objective\_property}\label{objective_property}}

\textbf{Elucidation:} A `property' that is determined by each `observer'
following a well defined `observation' procedure through a specific
perception channel.

\textbf{Comment:} The word objective does not mean that each observation
will provide the same results. It means that the observation followed a
well defined procedure.

\textbf{IRI:}
\url{http://emmc.info/emmo-properties\#EMMO_2a888cdf_ec4a_4ec5_af1c_0343372fc978}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{property}{property}
\end{itemize}

\hypertarget{qualitative_property}{%
\subsection{qualitative\_property}\label{qualitative_property}}

\textbf{Elucidation:} An `objective\_property' that cannot be
quantified.

\textbf{Example:} CFC is a `sign' that stands for the fact that the
morphology of atoms composing the microstructure of an entity is
predominantly Cubic Face Centered

\textbf{IRI:}
\url{http://emmc.info/emmo-physical-properties\#EMMO_909415d1_7c43_4d5e_bbeb_7e1910159f66}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{objective_property}{objective\_property}
\end{itemize}

\hypertarget{subjective_property}{%
\subsection{subjective\_property}\label{subjective_property}}

\textbf{Elucidation:} A `property' that cannot be univocally determined
and depends on an agent (e.g.~a human individual, a community) acting as
black-box.

\textbf{Example:} The beauty of that girl. The style of your clothing.

\textbf{Comment:} The word subjective means that a non-well defined or
an unknown procedure is used for the definition of the property.

This happens due to e.g.~the complexity of the object, the lack of a
underlying model for the representation of the object, the non-well
specified meaning of the property symbols.

A `subjective\_property' cannot be used to univocally compare
`object'-s.

e.g.~you cannot evaluate the beauty of a person on objective basis.

\textbf{IRI:}
\url{http://emmc.info/emmo-properties\#EMMO_251cfb4f_5c75_4778_91ed_6c8395212fd8}

\textbf{Relations:}

\begin{itemize}
\tightlist
\item
  is\_a \protect\hyperlink{property}{property}
\end{itemize}

\hypertarget{appendix}{%
\chapter{Appendix}\label{appendix}}

\begin{figure}
\centering
\includegraphics{/home/friisj/Private/prosjekter/EMMC/EMMO-python/examples/emmodoc/output/html_files/entity_graph.pdf}
\caption{The complete EMMO taxonomy.}
\end{figure}

\begin{figure}
\centering
\includegraphics{/home/friisj/Private/prosjekter/EMMC/EMMO-python/examples/emmodoc/output/html_files/relations_graph.pdf}
\caption{EMMO relations.}
\end{figure}

\end{document}

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