def test_convert_to_cnf(self):
statement = Not(Iff(Symbol("a"), Symbol("c")))
statement = converter.convert_formula(statement)
a_symbol = Symbol("a")
c_symbol = Symbol("c")
expected = And(
And(Or(c_symbol, a_symbol), Or(Not(a_symbol), a_symbol)),
And(Or(c_symbol, Not(c_symbol)), Or(Not(a_symbol), Not(c_symbol))))
self.assertEqual(expected, statement)
def test_print_cnf_list(self):
cnf = list()
a_symbol = Symbol("a")
b_symbol = Symbol("b")
not_a = Not(a_symbol)
not_b = Not(b_symbol)
cnf.append([a_symbol, b_symbol])
cnf.append([not_b, a_symbol])
cnf.append([not_a, not_b])
writer = StringIO()
util.print_cnf_list(cnf, out=writer)
cnf_list = "[[a, b], [~b, a], [~a, ~b]]\n"
self.assertEqual(cnf_list, writer.getvalue())
def perform_annihilation(statement):
change = False
if isinstance(statement, GeneralizedOr):
i = 0
while i < len(statement.args):
statement.args[i], change_new = perform_annihilation(
statement.args[i])
if isinstance(statement.args[i], Contradiction):
del statement.args[i]
i -= 1
i += 1
change = (change_new or change)
if len(statement.args) == 0:
return Contradiction(), True
elif isinstance(statement, GeneralizedAnd):
i = 0
while i < (len(statement.args) - 1):
if isinstance(statement.args[i], Not):
negate = statement.args[i].args[0]
else:
negate = Not(statement.args[i])
j = i + 1
while j < len(statement.args):
if negate == statement.args[j]:
return Contradiction(), True
j += 1
i += 1
return statement, change
def __init__(self, formulas, goal):
self.root = TreeNode()
for formula in formulas:
self.root.formulas.append(TreeFormula(formula))
self.root.formulas.append(TreeFormula(Not(goal)))
self.count = 1
self.expand_tree()
def _adjacency_helper(symbols):
return_list = []
"""
[a, b, c]
[[a, b, c], [a, b, ~c], [a, ~b, c], ...]
"""
for i in symbols:
if len(return_list) == 0:
return_list.append([i])
return_list.append([Not(i)])
else:
temp = deepcopy(return_list)
for j in range(len(return_list)):
return_list[j].append(i)
for j in range(len(temp)):
return_list.append(temp[j] + [Not(i)])
return return_list
def add_goal(self, statement):
"""
:param statement:
:return:
"""
statement = parser.parse(statement)
self._add_statement(deepcopy(statement), self.goals)
self._add_statement(Not(deepcopy(statement)), self._goals)
def add_formula(self, formula, count):
if self.closed:
return False
self.formulas.append(formula)
to_check = Not(formula.formula) if not isinstance(
formula.formula, Not) else formula.formula.args[0]
if self.has_formula(to_check):
self.closed = True
self.number = count
return True
return False
def negate_formula(formula):
"""
Negate the formula (or removing the Not if it's the outermost Operator)
:param formula: formula
:return: Negated formula
"""
if isinstance(formula, Not):
return formula.args[0]
elif isinstance(formula, Formula):
return Not(formula)
else:
raise TypeError(str(formula) + " is not a valid formula")
def distribute_not(statement):
"""
Distribute not over and/or clauses (flipping them)
:param statement:
:return:
"""
if isinstance(statement, Symbol):
return statement, False
args = statement.args
change = False
if isinstance(statement, Not):
if isinstance(args[0], And) or isinstance(args[0], Or) \
or isinstance(args[0], GeneralizedOr) or isinstance(args[0], GeneralizedAnd):
new_type = GeneralizedOr
if isinstance(args[0], Or) or isinstance(args[0], GeneralizedOr):
new_type = GeneralizedAnd
new_args = []
for arg in args[0].args:
new_args.append(Not(arg))
statement = new_type(*new_args)
change = True
elif isinstance(args[0], Not):
statement = args[0].args[0]
change = True
"""
elif isinstance(args[0], Quantifier):
new_type = Existential
if isinstance(args[0], Existential):
new_type = Universal
statement = new_type(args[0].symbol, Not(args[0].args[0]))
statement.args[0] = _distribute_not(statement.args[0])
"""
else:
for i in range(len(args)):
args[i], change = distribute_not(args[i])
if change:
break
return statement, change
def convert_if(statement):
"""
Convert conditional (A -> B) into (~A or B)
:param statement:
:return:
"""
if isinstance(statement, Symbol) or isinstance(statement, Not):
return statement, False
change = False
args = statement.args
for i in range(len(args)):
args[i], change = convert_if(args[i])
if change is True:
break
if change is False and isinstance(statement, If):
statement = GeneralizedOr(Not(deepcopy(args[0])), deepcopy(args[1]))
change = True
return statement, change
def test_is_tautology(self):
cnf = list()
cnf.append(Symbol("a"))
cnf.append(Not(Symbol("a")))
is_taut = util.is_tautology(cnf)
self.assertTrue(is_taut)
def test_negate_not(self):
negate = util.negate_formula(Not(Symbol("a")))
self.assertEqual(Symbol("a"), negate)
def test_non_equality_2(self):
statement_1 = Not(Symbol("b"))
statement_2 = Symbol("a")
self.assertNotEqual(statement_1, statement_2)
def test_symbol_lt_operator_1(self):
self.assertLess(Symbol('a'), Not(Symbol('a')))
def test_cnf_negation(self):
statement = Not(Not(And(Symbol("a"), Symbol("b"))))
statement = converter.convert_formula(statement)
expected = And(Symbol("a"), Symbol("b"))
self.assertEqual(expected, statement)
def test_operator_not_lt_symbol(self):
self.assertFalse(Not(Symbol("a")) < Symbol("b"))
def test_parse_iff_2(self):
statement = parser.parse("iff(not(A), not(B))")
self.assertEqual(statement, Iff(Not(Symbol("A")), Not(Symbol("B"))))
def test_cnf_not_distribution_2(self):
statement = Not(
Or(And(Symbol("a"), Not(Symbol("b"))), Not(Symbol("c"))))
statement = converter.convert_formula(statement)
expected = And(Or(Not(Symbol("a")), Symbol("b")), Symbol("c"))
self.assertEqual(expected, statement)
def test_operator_le_symbol(self):
self.assertLessEqual(Not(Symbol('a')), Not(Symbol('b')))
def expand_formula(self, tree_formula, tree_node):
tree_formula.number = self.count
tree_formula.broken = True
self.count += 1
formula = tree_formula.formula
if isinstance(formula, Not):
if isinstance(formula.args[0], Not):
children_nodes = tree_node.get_children()
for child_node in children_nodes:
self.add_formula(child_node, formula.args[0].args[0])
elif isinstance(formula.args[0], And):
left_nodes, right_nodes = tree_node.add_children()
for left_node in left_nodes:
self.add_formula(left_node, Not(formula.args[0].args[0]))
for right_node in right_nodes:
self.add_formula(right_node, Not(formula.args[0].args[1]))
elif isinstance(formula.args[0], Or):
children_nodes = tree_node.get_children()
for child_node in children_nodes:
for i in range(2):
if self.add_formula(child_node,
Not(formula.args[0].args[i])):
break
elif isinstance(formula.args[0], If):
children_nodes = tree_node.get_children()
for child_node in children_nodes:
if self.add_formula(child_node, formula.args[0].args[0]):
continue
self.add_formula(child_node, Not(formula.args[0].args[1]))
elif isinstance(formula.args[0], Iff):
left_nodes, right_nodes = tree_node.add_children()
for left_node in left_nodes:
if self.add_formula(left_node, formula.args[0].args[0]):
continue
self.add_formula(left_node, Not(formula.args[0].args[1]))
for right_node in right_nodes:
if self.add_formula(right_node,
Not(formula.args[0].args[0])):
continue
self.add_formula(right_node, formula.args[0].args[1])
elif isinstance(formula, And):
children_nodes = tree_node.get_children()
for child_node in children_nodes:
for i in range(2):
if self.add_formula(child_node, formula.args[i]):
break
elif isinstance(formula, Or):
left_nodes, right_nodes = tree_node.add_children()
for left_node in left_nodes:
self.add_formula(left_node, formula.args[0])
for right_node in right_nodes:
self.add_formula(right_node, formula.args[1])
elif isinstance(formula, If):
left_nodes, right_nodes = tree_node.add_children()
for left_node in left_nodes:
self.add_formula(left_node, Not(formula.args[0]))
for right_node in right_nodes:
self.add_formula(right_node, formula.args[1])
elif isinstance(formula, Iff):
left_nodes, right_nodes = tree_node.add_children()
for left_node in left_nodes:
for i in range(2):
if self.add_formula(left_node, formula.args[i]):
break
for right_node in right_nodes:
for i in range(2):
if self.add_formula(right_node, Not(formula.args[i])):
break
def test_operator_gt_symbol(self):
self.assertGreater(Not(Symbol("a")), Symbol("b"))
def test_not(self):
statement_a = Symbol('a')
statement_not = Not(statement_a)
self.assertEqual(statement_not.arity, 1)
self.assertEqual(repr(statement_not), "not(a)")
self.assertEqual(str(statement_not), "~a")
def test_operator_ge_symbol(self):
self.assertGreaterEqual(Not(Symbol("a")), Not(Symbol("a")))
def test_cnf_converter_equiv(self):
statement = Iff(Symbol("a"), Symbol("b"))
statement = converter.convert_formula(statement)
expected = And(Or(Not(Symbol("a")), Symbol("b")),
Or(Not(Symbol("b")), Symbol("a")))
self.assertEqual(expected, statement)
def test_parse_not(self):
statement = parser.parse("not(a)")
self.assertEqual(statement, Not(Symbol("a")))