def test_variables_classification():
tw = tarskiworld.create_small_world()
x = tw.variable('x', tw.Object)
y = tw.variable('y', tw.Object)
s = neg(land(tw.Cube(x), exists(y, land(tw.Tet(x), tw.LeftOf(x, y)))))
free = free_variables(s)
assert len(free) == 1 and symref(free[0]) == symref(x)
assert len(all_variables(s)) == 2
def test_detect_free_variables():
tw = tarskiworld.create_small_world()
x = tw.variable('x', tw.Object)
y = tw.variable('y', tw.Object)
s = neg(land(tw.Cube(x), exists(y, land(tw.Tet(x), tw.LeftOf(x, y)))))
v = CollectFreeVariables(tw)
s.accept(v)
assert len(list(v.free_variables)) == 1
def test_nnf_LPL_page_321_antecedent():
tw = tarskiworld.create_small_world()
x = tw.variable('x', tw.Object)
y = tw.variable('y', tw.Object)
s = forall(x, neg(land(tw.Cube(x), exists(y, land(tw.Tet(x), tw.LeftOf(x, y))))))
result = NNFTransformation.rewrite(s)
gamma = forall(x, lor(neg(tw.Cube(x)), forall(y, lor(neg(tw.Tet(x)), neg(tw.LeftOf(x, y))))))
assert str(result.nnf) == str(gamma)
def create_small_world_elements(numobjects=3):
lang = tarskiworld.create_small_world()
x, y = lang.variable('x', lang.Object), lang.variable('y', lang.Object)
_ = [
lang.constant(f'obj{i}', lang.Object)
for i in range(1, numobjects + 1)
]
return lang, x, y
def test_quantifier_elimination_fails_due_to_no_constants():
tw = tarskiworld.create_small_world()
x = tw.variable('x', tw.Object)
y = tw.variable('y', 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))
with pytest.raises(TransformationError):
QuantifierElimination.rewrite(tw, phi, QuantifierEliminationMode.All)
def test_symbol_ref_in_sets_equality_is_exact_syntactic_match():
tw = tarskiworld.create_small_world()
x = tw.variable('x', tw.Object)
y = tw.variable('y', tw.Object)
x_ref = symref(x)
y_ref = symref(y)
S = set()
S.add(x_ref)
assert y_ref not in S
assert x_ref in S
S.remove(x_ref)
assert len(S) == 0
def test_prenex_lpl_page_321():
tw = tarskiworld.create_small_world()
x = tw.variable('x', tw.Object)
y = tw.variable('y', 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))
result = PrenexTransformation.rewrite(tw, phi)
yp = tw.variable("y'", tw.Object)
gamma = NNFTransformation.rewrite(exists(yp, forall(
x, y, implies(land(tw.Cube(x), land(tw.Tet(y), tw.LeftOf(x, y))), land(tw.Dodec(yp), tw.BackOf(x, yp)))))).nnf
assert str(result.prenex) == str(gamma)
def test_cnf_conversion_easy():
tw = tarskiworld.create_small_world()
obj1 = tw.constant('obj1', tw.Object)
obj2 = tw.constant('obj2', tw.Object)
_ = tw.constant('obj3', tw.Object)
s1 = land(tw.Cube(obj1), neg(tw.Tet(obj2)))
s2 = land(tw.Cube(obj2), neg(tw.Tet(obj1)))
phi = lor(s1, s2)
c1 = lor(tw.Cube(obj1), tw.Cube(obj2))
c2 = lor(tw.Cube(obj1), neg(tw.Tet(obj1)))
c3 = lor(neg(tw.Tet(obj2)), tw.Cube(obj2))
c4 = lor(neg(tw.Tet(obj2)), neg(tw.Tet(obj1)))
psi = land(land(c1, c2), land(c3, c4))
result = CNFTransformation.rewrite(tw, phi)
assert str(result.cnf) == str(psi)
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 test_cnf_conversion_complex():
tw = tarskiworld.create_small_world()
x = tw.variable('x', tw.Object)
y = tw.variable('y', tw.Object)
obj1 = tw.constant('obj1', tw.Object)
obj2 = tw.constant('obj2', tw.Object)
obj3 = 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))
result = UniversalQuantifierElimination.rewrite(tw, phi)
result2 = CNFTransformation.rewrite(tw, result.universal_free.formula)
# print(result2.cnf)
# print('\n'.join( [ ','.join([str(l) for l in c]) for c in result2.clauses ] ) )
# print(len(result2.clauses))
assert len(result2.clauses) == 34
def test_universal_elimination_works():
tw = tarskiworld.create_small_world()
x = tw.variable('x', tw.Object)
y = tw.variable('y', tw.Object)
obj1 = tw.constant('obj1', tw.Object)
obj2 = tw.constant('obj2', tw.Object)
obj3 = 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 = UniversalQuantifierElimination.rewrite(tw, phi)
# print(str(result.universal_free))
result2 = UniversalQuantifierElimination.rewrite(tw, result.universal_free)
# print(str(result2.universal_free))
assert str(result.universal_free) == str(result2.universal_free)
def test_detect_free_variables():
tw = tarskiworld.create_small_world()
x = tw.variable('x', tw.Object)
y = tw.variable('y', tw.Object)
s = neg(land(tw.Cube(x), exists(y, land(tw.Tet(x), tw.LeftOf(x, y)))))
assert len(free_variables(s)) == 1
