def test_cnf_conversion_complex():
lang, x, y = create_small_world_elements(2)
s1 = exists(y, land(lang.Dodec(y), lang.BackOf(x, y)))
s2 = land(lang.Cube(x), exists(y, land(lang.Tet(y), lang.LeftOf(x, y))))
phi = forall(x, implies(s2, s1))
result = remove_quantifiers(lang, phi, QuantifierEliminationMode.All)
assert len(to_conjunctive_normal_form_clauses(lang, result)) == 30
# Now remove the quantifiers after tranforming to PNNF
result = remove_quantifiers(lang,
to_prenex_negation_normal_form(lang, phi),
QuantifierEliminationMode.All)
assert len(to_conjunctive_normal_form_clauses(lang, result)) == 126
def test_existential_elimination2():
lang, x, y = create_small_world_elements(2)
s1 = exists(y, land(lang.Dodec(y), lang.BackOf(x, y)))
s2 = land(lang.Cube(x), exists(y, land(lang.Tet(y), lang.LeftOf(x, y))))
phi = forall(x, implies(s2, s1))
result = remove_quantifiers(lang, phi, QuantifierEliminationMode.All)
assert is_quantifier_free(result)
def test_universal_elimination_works():
tw = tarskiworld.create_small_world()
x = tw.variable('x', tw.Object)
y = tw.variable('y', tw.Object)
_ = tw.constant('obj1', tw.Object)
_ = tw.constant('obj2', tw.Object)
_ = tw.constant('obj3', tw.Object)
s1 = exists(y, land(tw.Dodec(y), tw.BackOf(x, y)))
s2 = land(tw.Cube(x), exists(y, land(tw.Tet(y), tw.LeftOf(x, y))))
phi = forall(x, implies(s2, s1))
# print(str(phi))
result = remove_quantifiers(tw, phi, QuantifierEliminationMode.Forall)
result2 = remove_quantifiers(tw, result, QuantifierEliminationMode.Forall)
assert str(result) == str(result2)
def fully_ground(smtlang, f, horizon):
phi = remove_quantifiers(smtlang, f, QuantifierEliminationMode.All)
phi = Simplify().simplify_expression(phi)
if phi is False:
raise RuntimeError(
f'Formula {phi} simplified to False, hence the theory is not satisfiable'
)
return phi
def test_cnf_conversion_complex():
lang, x, y = create_small_world_elements(2)
s1 = exists(y, land(lang.Dodec(y), lang.BackOf(x, y)))
s2 = land(lang.Cube(x), exists(y, land(lang.Tet(y), lang.LeftOf(x, y))))
phi = forall(x, implies(s2, s1))
result = remove_quantifiers(lang, phi, QuantifierEliminationMode.All)
transf = CNFTransformation.rewrite(lang, result)
# print(transf.cnf)
# print('\n'.join([','.join([str(l) for l in c]) for c in transf.clauses]))
assert len(transf.clauses) == 30
# Now remove the quantifiers after tranforming to PNNF
result = remove_quantifiers(lang,
to_prenex_negation_normal_form(lang, phi),
QuantifierEliminationMode.All)
transf = CNFTransformation.rewrite(lang, result)
assert len(transf.clauses) == 126
def test_existential_elimination1():
lang, x, y = create_small_world_elements(2)
obj1, obj2 = lang.get("obj1"), lang.get("obj2")
phi = exists(y, land(lang.Dodec(y), lang.BackOf(x, y)))
result = remove_quantifiers(lang, phi, QuantifierEliminationMode.Exists)
# We cannot guarantee in which order the expansion of the exists will be done, so we check for both possibilities:
assert result == (lang.Dodec(obj1) & lang.BackOf(x, obj1)) | (lang.Dodec(obj2) & lang.BackOf(x, obj2)) or \
result == (lang.Dodec(obj2) & lang.BackOf(x, obj2)) | (lang.Dodec(obj1) & lang.BackOf(x, obj1))