#Predicate Logic Without Negation
















    # Handle conjunction (∧)

    # Handle implication (→)



    # Define the truth value for each predicate and its corresponding terms
    # This can be modified based on the problem requirements


    # Handle other predicates...



# Example usage

# Example formula: P(x, y) ∧ Q(y, x)



if __name__ == '__main__':
    import itertools
    class Predicate:
        def __init__(self, name, arity):
            self.name = name
            self.arity = arity
        def __repr__(self):
            return self.name
    class Term:
        def __init__(self, name):
            self.name = name
        def __repr__(self):
            return self.name
    class Atom:
        def __init__(self, predicate, terms):
            self.predicate = predicate
            self.terms = terms
        def __repr__(self):
            terms_str = ", ".join(str(term) for term in self.terms)
            return f"{self.predicate}({terms_str})"
    def is_formula_satisfiable(formula, domain):
        for assignment in itertools.product(*domain):
            assignment_dict = {term.name: value for term, value in zip(domain, assignment)}
            if evaluate_formula(formula, assignment_dict):
                return True
        return False
    def evaluate_formula(formula, assignment):
        if isinstance(formula, Atom):
            return evaluate_atom(formula, assignment)
        if len(formula) > 1:
            return all(evaluate_formula(subformula, assignment) for subformula in formula)
        antecedent, consequent = formula[0]
        return not evaluate_formula(antecedent, assignment) or evaluate_formula(consequent, assignment)
    def evaluate_atom(atom, assignment):
        predicate = atom.predicate
        terms = atom.terms
        if predicate.name == "P":
            return terms[0].name == terms[1].name
        if predicate.name == "Q":
            return terms[0].name != terms[1].name
        raise ValueError("Unknown predicate:", predicate)
    domain = [Term("x"), Term("y")]
    formula = [
        Atom(Predicate("P", 2), [domain[0], domain[1]]),
        Atom(Predicate("Q", 2), [domain[1], domain[0]])
    ]
    is_satisfiable = is_formula_satisfiable(formula, domain)
    print("Is formula satisfiable:", is_satisfiable)
