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Brandon Rozek 2025-11-25 10:03:55 -05:00
parent 0a894388a0
commit 7e4a570407
1 changed files with 30 additions and 24 deletions
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54
vsp.py
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@ -43,10 +43,10 @@ def has_vsp(model: Model, impfunction: ModelFunction,
top = model.ordering.top()
bottom = model.ordering.bottom()
# Cache of closures
C: Dict[ModelValue, Set[ModelValue]] = {}
for x in model.designated_values:
# Discard ({⊥} ∪ A', B) subalgebras
if bottom is not None and x == bottom:
continue
@ -55,19 +55,31 @@ def has_vsp(model: Model, impfunction: ModelFunction,
if top is not None and negation_defined and x == top:
continue
if x not in C:
C[x] = model_closure({x,}, model.logical_operations, None)
Xs = C[x]
candidate_ys = [y for y in model.designated_values if impfunction(x, y) not in model.designated_values]
if len(candidate_ys) == 0:
continue
carrier_set_left: Set[ModelValue] = model_closure(C.get(x, {x,}), model.logical_operations, bottom)
C[x] = carrier_set_left
# Discard ({⊥} ∪ A', B) subalgebras
if bottom is not None and bottom in Xs:
if bottom is not None and bottom in carrier_set_left:
continue
# Discard ({⊤} ∪ A', B) subalgebras when negation is defined
if top is not None and negation_defined and top in Xs:
if top is not None and negation_defined and top in carrier_set_left:
continue
for y in candidate_ys:
# Discard ({a} ∪ A', {b} ∪ B') subalgebras when a <= b
if model.ordering.is_lt(x, y):
continue
# Discard ({a} ∪ A', {b} ∪ B') subalgebras when b <= a and negation is defined
if negation_defined and model.ordering.is_lt(y, x):
continue
for y in model.designated_values - Xs:
# Discard (A, {⊤} ∪ B') subalgebras
if top is not None and y == top:
@ -77,36 +89,30 @@ def has_vsp(model: Model, impfunction: ModelFunction,
if bottom is not None and negation_defined and y == bottom:
continue
# Discard ({a} ∪ A', {b} ∪ B') subalgebras when a <= b
if model.ordering.is_lt(x, y):
continue
# Discard ({a} ∪ A', {b} ∪ B') subalgebras when b <= a and negation is defined
if negation_defined and model.ordering.is_lt(y, x):
continue
if y not in C:
C[y] = model_closure({y,}, model.logical_operations, None)
Ys = C[y]
carrier_set_right: Set[ModelValue] = model_closure(C.get(y, {y,}), model.logical_operations, top)
C[y] = carrier_set_right
# Discard (A, {⊤} ∪ B') subalgebras
if top is not None and top in Ys:
if top is not None and top in carrier_set_right:
continue
# Discard (A, {⊥} ∪ B') subalgebras when negation is defined
if bottom is not None and negation_defined and bottom in Ys:
if bottom is not None and negation_defined and bottom in carrier_set_right:
continue
if not Xs.isdisjoint(Ys):
# Discard subalgebras that intersect
if not carrier_set_left.isdisjoint(carrier_set_right):
continue
# Check whether for all pairs in the subalgebra,
# that implication is falsified.
falsified = True
for (xi, yi) in product(Xs, Ys):
if impfunction(xi, yi) in model.designated_values:
for (x2, y2) in product(carrier_set_left, carrier_set_right):
if impfunction(x2, y2) in model.designated_values:
falsified = False
break
if falsified:
return VSP_Result(True, model.name, Xs, Ys)
return VSP_Result(True, model.name, carrier_set_left, carrier_set_right)
return VSP_Result(False, model.name)