# Updated Counterfactual Falsification Semantics

## Changes Made

### 1. Updated extended_falsify Logic

The falsification condition was changed from:
- ∃v ∃t : (max_compatible(t,s,v) ∧ ∃f : compatible(t.v, f))

To:
- ∃v : (verify(v,A) ∧ ∀t : (max_compatible(t,s,v) → ∃f : compatible(t.v, f)))

This means a state falsifies a counterfactual only if there exists a verifier of A such that **all** maximal compatible parts (not just one) lead to compatibility with some falsifier of B.

### 2. Updated find_verifiers_and_falsifiers

The implementation now:
- Collects all maximal compatible parts for each verifier
- For falsification: checks that ALL maximal parts lead to compatibility with some B falsifier
- For verification: maintains the original logic (no maximal part can lead to compatibility with B falsifiers)

### 3. Removed Fusion Closure

Per your request, the explicit fusion closure enforcement has been removed. The semantics should naturally respect fusion closure through the verification/falsification conditions themselves.

## Impact

### Fewer Falsifiers
With the stricter falsification condition, fewer states falsify counterfactuals. A state must now have the property that for some A-verifier, every way of combining with it leads to B being possibly false.

### Null State Still a Falsifier
In the example, the null state (□) remains a falsifier because:
- For verifier b of A
- The only maximal compatible part of □ with b is □ itself
- The fusion □ ∪ b = b
- b is compatible with the B falsifier a
- Since ALL maximal parts (just one in this case) lead to compatibility, □ falsifies

### Test Compatibility
All 33 existing tests continue to pass, indicating the refined semantics is compatible with the expected logical behavior.

## Semantic Interpretation

The updated falsification condition captures a stronger notion: a state falsifies a counterfactual if there's an A-verifier such that no matter how we maximally extend the state to be compatible with that verifier, we always end up with something that could make B false.

This is more restrictive than the previous "there exists a way" interpretation, leading to fewer falsifiers while maintaining logical consistency.