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prover.py
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prover.py
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import random
import re
import itertools
import time
OPS = ["IF", "AND", "OR", "NOT", "IMPLIES"]
QUANTS = ["FORALL", "EXISTS"]
def getElement(xtype, xvalue):
return (xtype, xvalue)
def remove_conditionals(FOL_Tree):
_symbol_type = FOL_Tree.get_element_type()
_symbol_value = FOL_Tree.get_element_value()
_child_nodes = FOL_Tree.get_child_nodes()
if _symbol_type == "op" and _symbol_value == "IMPLIES":
_symbol_value = "OR"
FOL_Tree.set_node(_symbol_type, _symbol_value)
_child_node = _child_nodes[-1]
# _child_symbol_type=child_node.get_element_type()
# _child_symbol_value=child_node.get_element_value()
new_symbol_type = "op"
new_symbol_value = "NOT"
_new_node = Node(new_symbol_type, new_symbol_value)
_new_node.add_child(_child_node)
_child_nodes[-1] = _new_node
FOL_Tree.set_child_nodes(_child_nodes)
_child_nodes = FOL_Tree.get_child_nodes()
for i in range(len(_child_nodes)):
remove_conditionals(_child_nodes[i])
return FOL_Tree
def deMorgan(FOL_Tree):
_current_node = FOL_Tree
_symbol_type = FOL_Tree.get_element_type()
_symbol_value = FOL_Tree.get_element_value()
_child_nodes = FOL_Tree.get_child_nodes()
if _symbol_type == "op" and _symbol_value == "NOT":
_child_node = _child_nodes[0]
_child_symbol_type = _child_node.get_element_type()
_child_symbol_value = _child_node.get_element_value()
# _symbol_value="OR"
# FOL_Tree.set_node(_symbol_type,_symbol_value)
new_symbol_type = new_symbol_value = ""
if _child_symbol_type == "op":
new_symbol_type = "op"
if _child_symbol_value == "AND":
new_symbol_value = "OR"
elif _child_symbol_value == "OR":
new_symbol_value = "AND"
elif _child_symbol_type == "quant":
new_symbol_type = "quant"
if _child_symbol_value == "FORALL":
new_symbol_value = "EXISTS"
elif _child_symbol_value == "EXISTS":
new_symbol_value = "FORALL"
if new_symbol_type != "" and new_symbol_value != "":
FOL_Tree.set_node(new_symbol_type, new_symbol_value)
_child_child_nodes = _child_node.get_child_nodes()
_new_children = []
for _child_child_node in _child_child_nodes:
_child_child_symbol_type = _child_child_node.get_element_type()
_child_child_symbol_value = _child_child_node.get_element_value()
if _child_child_symbol_type == "variable":
_new_children.append(_child_child_node)
else:
_new_node = Node(_symbol_type, _symbol_value)
_new_node.add_child(_child_child_node)
_new_children.append(_new_node)
FOL_Tree.set_child_nodes(_new_children)
_child_nodes = FOL_Tree.get_child_nodes()
for i in range(len(_child_nodes)):
deMorgan(_child_nodes[i])
return FOL_Tree
def standardize(FOL_Tree, variable_names={}):
_symbol_type = FOL_Tree.get_element_type()
_symbol_value = FOL_Tree.get_element_value()
_child_nodes = FOL_Tree.get_child_nodes()
if _symbol_type == "quant":
_child_node = _child_nodes[-1]
_child_symbol_type = _child_node.get_element_type()
_child_symbol_value = _child_node.get_element_value()
variable_names[_child_symbol_value] = _child_symbol_value + "_" + str(random.randint(0, 10000))
_child_node.set_node(_child_symbol_type, variable_names[_child_symbol_value])
_child_nodes[-1] = _child_node
elif _symbol_type == "function" or _symbol_type == "predicate":
for i in range(len(_child_nodes)):
_child_node = _child_nodes[i]
_child_symbol_type = _child_node.get_element_type()
_child_symbol_value = _child_node.get_element_value()
if _child_symbol_value in variable_names:
_child_node.set_node(_child_symbol_type, variable_names[_child_symbol_value])
_child_nodes[i] = _child_node
FOL_Tree.set_child_nodes(_child_nodes)
for i in range(len(_child_nodes)):
standardize(_child_nodes[i], variable_names)
return FOL_Tree
def recorrect(FOL_Tree):
_symbol_type = FOL_Tree.get_element_type()
_symbol_value = FOL_Tree.get_element_value()
_child_nodes = FOL_Tree.get_child_nodes()
for i in range(len(_child_nodes)):
_child_node=_child_nodes[i]
_child_node_symbol_type = _child_node.get_element_type()
_child_node_symbol_value = _child_node.get_element_value()
if (_symbol_type == "function"):
if (_child_node_symbol_type == "function"):
_symbol_type = "predicate"
FOL_Tree.set_node(_symbol_type, _symbol_value)
if (_symbol_type == "op" or _symbol_type == "quant"):
if (_child_node_symbol_type == "function"):
_child_node_symbol_type = "predicate"
_child_node.set_node(_child_node_symbol_type,_child_node_symbol_value)
_child_nodes[i]=_child_node
if (_symbol_type == "predicate"):
if (_child_node_symbol_type == "symbol"):
_child_node_symbol_type = "variable"
_child_node.set_node(_child_node_symbol_type, _child_node_symbol_value)
_child_nodes[i] = _child_node
recorrect(_child_node)
FOL_Tree.set_child_nodes(_child_nodes)
return FOL_Tree
def isCNF(FOL_Tree):
_symbol_type = FOL_Tree.get_element_type()
_symbol_value = FOL_Tree.get_element_value()
_child_nodes = FOL_Tree.get_child_nodes()
if (_symbol_type == "op" and _symbol_value == "AND"):
for i in range(len(_child_nodes)):
_child_node=_child_nodes[i]
_child_node_symbol_type = _child_node.get_element_type()
_child_node_symbol_value = _child_node.get_element_value()
if not (_child_node_symbol_type == "op" and _child_node_symbol_value == "OR"):
return False
_child_child_nodes =_child_node.get_child_nodes()
for i in range(len(_child_child_nodes)):
_child_child_node = _child_child_nodes[i]
_child_child_node_symbol_type = _child_child_node.get_element_type()
_child_child_node_symbol_value = _child_child_node.get_element_value()
if (_child_child_node_symbol_type == "op" and (_child_child_node_symbol_value == "AND" or _child_child_node_symbol_value == "OR")):
return False
else:
return False
return True
def isClause(FOL_Tree):
_symbol_type = FOL_Tree.get_element_type()
_symbol_value = FOL_Tree.get_element_value()
_child_nodes = FOL_Tree.get_child_nodes()
if (_symbol_type == "op" and _symbol_value == "OR"):
for i in range(len(_child_nodes)):
_child_node = _child_nodes[i]
_child_node_symbol_type = _child_node.get_element_type()
_child_node_symbol_value = _child_node.get_element_value()
if _child_node_symbol_type == "op" and _child_node_symbol_value == "NOT":
continue;
elif _child_node_symbol_type == "predicate":
continue;
else:
return False
else:
return False
return True
def isLiteral(FOL_Tree):
_symbol_type = FOL_Tree.get_element_type()
_symbol_value = FOL_Tree.get_element_value()
_child_nodes = FOL_Tree.get_child_nodes()
if (_symbol_type == "op" and _symbol_value == "NOT"):
_child_node = _child_nodes[0]
_child_node_symbol_type = _child_node.get_element_type()
_child_node_symbol_value = _child_node.get_element_value()
if _child_node_symbol_type == "predicate":
return True
if _symbol_type == "predicate":
return True
return False
def concatenate(node_tuple):
_new_children=[]
for node in node_tuple:
_new_children.extend(node.get_child_nodes())
parent=Node("op","OR")
parent.set_child_nodes(_new_children)
return parent
def convertToCNF(FOL_Tree):
_symbol_type = FOL_Tree.get_element_type()
_symbol_value = FOL_Tree.get_element_value()
_child_nodes = FOL_Tree.get_child_nodes()
_no_child_nodes=len(_child_nodes)
## CNF check
if isCNF(FOL_Tree):
return FOL_Tree
## clause
if isClause(FOL_Tree):
_new_FOL_Tree = Node("op", "AND")
_new_FOL_Tree.set_child_nodes([FOL_Tree])
return _new_FOL_Tree
## Literal
if isLiteral(FOL_Tree):
_new_FOL_Tree = Node("op", "AND")
_new_parent_node=Node("op", "OR")
_new_parent_node.set_child_nodes([FOL_Tree])
_new_FOL_Tree.set_child_nodes([_new_parent_node])
return _new_FOL_Tree
if _symbol_type == "op" and _symbol_value == "AND" and _no_child_nodes>0:
_new_children=[]
for i in range(len(_child_nodes)):
_child_node =_child_nodes[i]
X_Tree = convertToCNF(_child_node)
x_child_nodes = X_Tree.get_child_nodes()
for x_child_node in x_child_nodes:
_new_children.append(x_child_node)
_new_FOL_Tree=Node("op", "AND")
_new_FOL_Tree.set_child_nodes(_new_children)
return _new_FOL_Tree
if _symbol_type == "op" and _symbol_value == "OR" and _no_child_nodes > 0:
_new_children = []
for i in range(len(_child_nodes)):
_child_node = _child_nodes[i]
X_Tree = convertToCNF(_child_node)
x_child_nodes=X_Tree.get_child_nodes()
_x_children=[]
for x_child_node in x_child_nodes:
_x_children.append(x_child_node)
_new_children.append(_x_children)
_new_combined_children=list(itertools.product(*_new_children))
_new_x_children=[]
for node_tuple in _new_combined_children:
_new_x_node=concatenate(node_tuple)
_new_x_children.append(_new_x_node)
_new_FOL_Tree = Node("op", "AND")
_new_FOL_Tree.set_child_nodes(_new_x_children)
return _new_FOL_Tree
else:
print("Error.")
class Node:
def __init__(self, element_type, element_value):
self.set_node(element_type, element_value)
self.children = []
def add_child(self, x_node):
self.children.append(x_node)
def set_child_nodes(self, children):
self.children = children
def get_child_nodes(self):
return self.children
def set_node(self, element_type, element_value):
self.element_type = element_type
self.element_value = element_value
def get_element_type(self):
return self.element_type
def get_element_value(self):
return self.element_value
def get_text(self):
return "[" + self.get_element_type() + "] " + self.get_element_value()
def __str__(self, level=0):
text = "--" * level + self.get_text() + "\n"
for child_node in self.children:
text += child_node.__str__(level + 1)
return text
def printTree(node):
node.get_child_nodes()
def parse_tree(args):
_stack = []
_stack_element = None
for index in range(len(args)):
current_index = index
current_element = args[current_index]
current_symbol_type = current_element[0]
current_symbol_value = current_element[1]
if current_symbol_type == "open_bracket" and current_symbol_value == "(":
continue
elif current_symbol_type == "close_bracket" and current_symbol_value == ")":
_picked_child_nodes = []
while True:
_parent_node = _stack.pop()
_symbol_type = _parent_node.get_element_type()
_symbol_value = _parent_node.get_element_value()
if _symbol_type == "op" or _symbol_type == "quant" or _symbol_type == "function" or _symbol_type == "predicate":
_child_nodes = _parent_node.get_child_nodes()
_no_child_nodes = len(_child_nodes)
if _no_child_nodes == 0:
break
_picked_child_nodes.append(_parent_node)
_parent_node.set_child_nodes(_picked_child_nodes)
_stack.append(_parent_node)
else:
_node = Node(current_symbol_type, current_symbol_value)
_stack.append(_node)
assert (len(_stack) == 1)
return _stack.pop()
def parse(F):
characters = F
# breaking the input to argument types
# argument types: open and close bracket, operator and symbol
args = []
regex = r'''\(|\)|\[|\]|\-?\d+\.\d+|\-?\d+|[^,(^)\s]+'''
# sanitizing the input
characters = characters.replace("\t", " ")
characters = characters.replace("\n", " ")
characters = characters.replace("\r", " ")
characters = characters.lstrip(" ")
characters = characters.rstrip(" ")
##prev_arg_name = None
prev_arg = next_arg = None
lines = []
arg_list = re.findall(regex, characters)
for i in range(len(arg_list)):
arg = arg_list[i]
if (i - 1 >= 0):
prev_arg = arg_list[i - 1]
if (i + 1 < len(arg_list)):
next_arg = arg_list[i + 1]
if (arg == "("):
arg_name = "open_bracket"
elif (arg == ")"):
arg_name = "close_bracket"
elif prev_arg == "(":
if (arg in OPS):
arg_name = "op"
elif (arg in QUANTS):
arg_name = "quant"
else:
arg_name = "function"
elif (prev_arg in QUANTS):
arg_name = "variable"
elif arg.isalnum():
arg_name = "symbol"
arg_tuple = (arg_name, arg)
args.append(arg_tuple)
return parse_tree(args)
##################################################################################
def findIncSet(F):
result = []
for i in range(0, len(F)):
try:
F[i] = algorithm(F[i])
if F[i]:
result.append(i)
except BaseException:
continue
return result
def algorithm(L):
clauses = list()
for i in range(0, len(L)):
FOL_Tree = parse(L[i])
FOL_Tree = recorrect(FOL_Tree)
FOL_Tree = remove_conditionals(FOL_Tree)
FOL_Tree = deMorgan(FOL_Tree)
FOL_Tree = doubleNOT(FOL_Tree)
FOL_Tree = standardize(FOL_Tree)
FOL_Tree = prenex_form(FOL_Tree)
FOL_Tree = skolemize(FOL_Tree)
FOL_Tree = drop_universal(FOL_Tree)
FOL_Tree = symbol_fixer(FOL_Tree)
FOL_Tree = convertToCNF(FOL_Tree)
predicates = and_to_clausal(FOL_Tree)
clauses.append(predicates)
return resolution(clauses)
def doubleNOT(FOL_Tree):
currentNode = FOL_Tree
_symbol_value = currentNode.get_element_value()
if len(currentNode.get_child_nodes()) == 0:
return FOL_Tree
if _symbol_value == "NOT": #if current is NOT
child = currentNode.get_child_nodes()
child_value = child[0].get_element_value()
if child_value == "NOT": #if child is also not, set current to its child
currentNode.set_node(currentNode.get_child_nodes()[0].get_child_nodes()[0].get_element_type(), currentNode.get_child_nodes()[0].get_child_nodes()[0].get_element_value())
if len(currentNode.get_child_nodes()[0].get_child_nodes()[0].get_child_nodes()) == 2:
currentNode.get_child_nodes()[1] = currentNode.get_child_nodes()[0].get_child_nodes()[0].get_child_nodes()[1]
currentNode.get_child_nodes()[0] = currentNode.get_child_nodes()[0].get_child_nodes()[0].get_child_nodes()[0]
doubleNOT(currentNode)
if len(currentNode.get_child_nodes()) == 2:
doubleNOT(currentNode.get_child_nodes()[1])
doubleNOT(currentNode.get_child_nodes()[0])
return FOL_Tree
############### PRENEX CODE START ###################
# This function checks if its already in prenex form, if not it passes it to a converter.
def prenex_form(FOL_Tree):
# Prenex form is pushing all the quantifiers up as far as possible.
if_prenex = prenex_check(FOL_Tree)
if if_prenex:
return FOL_Tree
else:
FOL_Tree = prenex_convert(FOL_Tree)
return prenex_form(FOL_Tree)
def prenex_check(FOL_Tree):
_symbol_type = FOL_Tree.get_element_type()
_symbol_value = FOL_Tree.get_element_value()
currChildren = FOL_Tree.get_child_nodes()
# Check for lenghth of children here
if len(currChildren) != 2:
return True
leftChild = currChildren[1]
leftChildType = leftChild.get_element_type()
rightChild = currChildren[0]
rightChildType = rightChild.get_element_type()
if _symbol_type != "quant" and (leftChildType == "quant" or rightChildType == "quant"):
return False
else:
return prenex_check(leftChild) and prenex_check(rightChild)
def prenex_convert(FOL_Tree):
currentNode = FOL_Tree
_symbol_type = FOL_Tree.get_element_type()
_symbol_value = FOL_Tree.get_element_value()
currChildren = FOL_Tree.get_child_nodes()
if len(currChildren) != 2:
return FOL_Tree
leftChild = currChildren[1]
leftChildType = leftChild.get_element_type()
leftChildValue = leftChild.get_element_value()
leftChildChildren = leftChild.get_child_nodes()
rightChild = currChildren[0]
rightChildType = rightChild.get_element_type()
rightChildValue = rightChild.get_element_value()
rightChildChildren = rightChild.get_child_nodes()
if _symbol_type == "op" and leftChildType == "quant": #Left subtree is the issue.
leftChildLeft = leftChildChildren[1]
leftChildLeftType = leftChildLeft.get_element_type()
leftChildLeftValue = leftChildLeft.get_element_value()
tempType = currentNode.get_element_type()
tempValue = currentNode.get_element_value()
currentNode.set_node(leftChildType, leftChildValue)
leftChild.set_node(tempType, tempValue)
temp = Node(leftChildLeftType, leftChildLeftValue)
leftChild.get_child_nodes()[1] = leftChild.get_child_nodes()[0]
leftChild.get_child_nodes()[0] = currentNode.get_child_nodes()[0]
currentNode.get_child_nodes()[0] = currentNode.get_child_nodes()[1]
currentNode.get_child_nodes()[1] = temp
elif _symbol_type == "op" and rightChildType == "quant": #Right subtree is the issue.
rightChildLeft = rightChildChildren[1]
rightChildLeftType = rightChildLeft.get_element_type()
rightChildLeftValue = rightChildLeft.get_element_value()
tempType = currentNode.get_element_type()
tempValue = currentNode.get_element_value()
currentNode.set_node(rightChildType, rightChildValue)
rightChild.set_node(tempType, tempValue)
temp = Node(rightChildLeftType, rightChildLeftValue)
rightChild.get_child_nodes()[1] = currentNode.get_child_nodes()[1]
currentNode.get_child_nodes()[1] = temp
prenex_convert(leftChild)
prenex_convert(rightChild)
return FOL_Tree
################ PRENEX CODE END ##################
varList = []
def skolemize(FOL_Tree):
global varList
currentNode = FOL_Tree
_symbol_type = FOL_Tree.get_element_type()
_symbol_value = FOL_Tree.get_element_value()
if _symbol_type != "quant":
varList = []
return FOL_Tree
else:
currChildren = currentNode.get_child_nodes()
leftChild = currChildren[1]
leftChildValue = leftChild.get_element_value()
rightChild = currChildren[0]
rightChildType = rightChild.get_element_type()
rightChildValue = rightChild.get_element_value()
rightChildChildren = rightChild.get_child_nodes()
if len(rightChildChildren) == 2:
rightChildleft = rightChildChildren[1]
rightChildRight = rightChildChildren[0]
if _symbol_value == "FORALL":
varList.append(leftChildValue)
else: #EXISTS
if varList == []:
new_symbol_type = "symbol"
else:
new_symbol_type = "function"
rename(FOL_Tree, new_symbol_type, leftChildValue)
currentNode.set_node(rightChildType, rightChildValue)
if len(rightChildChildren) == 1:
currChildren.pop(1)
for i in range(0, len(rightChildChildren)):
currChildren[i] = rightChildChildren[i]
skolemize(currentNode)
skolemize(currChildren[0])
return FOL_Tree
def rename(FOL_Tree, new_symbol_type, var):
global varList
currentNode = FOL_Tree
currChildren = currentNode.get_child_nodes()
_symbol_type = FOL_Tree.get_element_type()
_symbol_value = FOL_Tree.get_element_value()
if _symbol_value == var:
if new_symbol_type == "symbol":
currentNode.set_node(new_symbol_type, var)
else: #new_symbol_type == "function"
currentNode.set_node(new_symbol_type, var)
for i in range(0, len(varList)):
temp = Node("variable", varList[i])
currentNode.add_child(temp)
else:
for i in range(len(currChildren)):
FOL_Tree = rename(currChildren[i], new_symbol_type, var)
return FOL_Tree
universal_varList = []
def drop_universal(FOL_Tree):
global universal_varList
_symbol_type = FOL_Tree.get_element_type()
currentNode = FOL_Tree
currChildren = currentNode.get_child_nodes()
if len(currChildren) != 2:
return FOL_Tree
else:
if _symbol_type == "quant":
leftChild = currChildren[1]
leftChildValue = leftChild.get_element_value()
universal_varList.append(leftChildValue)
rightChild = currChildren[0]
rightChildType = rightChild.get_element_type()
rightChildValue = rightChild.get_element_value()
rightChildChildren = rightChild.get_child_nodes()
currentNode.set_node(rightChildType, rightChildValue)
if len(rightChildChildren) == 1:
currChildren.pop(1)
for i in range(0, len(rightChildChildren)):
currChildren[i] = rightChildChildren[i]
drop_universal(currentNode)
drop_universal(currChildren[0])
return FOL_Tree
def symbol_fixer(FOL_Tree):
currentNode = FOL_Tree
if currentNode.get_element_type() == "variable":
if currentNode.get_element_value() not in universal_varList:
currentNode.set_node("symbol", currentNode.get_element_value())
if len(currentNode.get_child_nodes()) == 0:
return FOL_Tree
for i in range(0, len(currentNode.get_child_nodes())):
symbol_fixer(currentNode.get_child_nodes()[i])
return FOL_Tree
###################################################################################
VARIABLE = "VARIABLE"
CONSTANT = "CONSTANT"
class Argument(object):
def __init__(self, name, kind):
self._name = name
self._kind = kind
def is_variable(self):
return self._kind == VARIABLE
def is_constant(self):
return self._kind == CONSTANT
def get_name(self):
return self._name
def set_name(self, name):
self._name = name
def same_kind(self, arg):
"""
Check if the arguments is same
:param arg:
:return:
"""
return self._kind == arg._kind
def equals(self, arg):
"""
Checks if the arg and self are same argument
:param arg:
:return:
"""
return (self.same_kind(arg) and self._name == arg._name)
@classmethod
def make_var(cls, name):
return Argument(name, VARIABLE)
@classmethod
def make_const(cls, name):
return Argument(name, CONSTANT)
class Predicate(object):
"""
Represents a predicate like P(x, y) or -P(x, y)
Order of the args and constants matters
For a predicate P(x, a, y)
Name: P, Args: x, a, y; x is a var, a is constant and y is a var
"""
def __init__(self, name, args, negative=False):
"""
:param name: string
:param args: Argument objects
:param negative: bool
"""
self._name = name
self._args = args
self._negative = negative
def __str__(self):
s = "{0}({1})".format(self._name, ",".join([arg._name for arg in self._args]))
if self._negative:
return "-"+s
return s
def get_name(self):
return self._name
def get_args(self):
return self._args
def get_negative(self):
return self._negative
def same_formula(self, obj):
"""
Checks whether the self and obj has the same for i.e. P(x,y)
has same form as P(x,y) and -P(x,y), or P(y, x), or P(a, x)
:param obj: Predicate()
:return: bool
"""
if self._name != obj._name:
return False
if len(self._args) != len(obj._args):
return False
return True
def complement_of(self, obj):
"""
Checks whether the
:param obj: Predicate()
:return:
"""
return (self.same_formula(obj) and self._negative != obj._negative)
def same_args(self, obj):
"""
Checks if the args in self and obj are same
:param obj: Predicate()
:return:
"""
for i in range(0, len(obj._args)):
if not self._args[i].equals(obj._args[i]):
return False
return True
def equals(self, obj):
"""
Return true if both objects are P(x,y) and P(x,y)
:param obj: Predicate()
:return:
"""
if not self.same_formula(obj):
return False
if not self.same_args(obj):
return False
if self._negative != obj._negative:
return False
return True
def same_predicate(self, obj):
if self._name != obj._name:
return False
return True
def complement_of_predicate(self, obj):
if self.same_predicate(obj) == True and self._negative != obj._negative:
return True
return False
def unification(p1, p2, replacements):
"""
Takes a two predicates and tries for unifying them which are same, i.e. P(x1, y1) and -P(x1, y1)
returns None is couldn't be done else returns the list with unification, and,
a dict() with replacements
:param replacements:
:return: unifiable predicates, p1, p2 and bool if unification could be done or not
"""
p1_args = list(p1.get_args())
p2_args = list(p2.get_args())
if len(p1_args) != len(p2_args):
return p1, p2, False
if p1.same_args(p2): # return as it is
return p1, p2, True
for i in range(0, len(p1_args)):
p1_arg = p1_args[i]
p2_arg = p2_args[i]
if p2_arg.equals(p1_arg):
continue
if p1_arg.is_variable() and p2_arg.is_variable(): # Replace p2 by p1
token = replacements.get(p2_arg.get_name(), '')
if token == '':
token = p1_arg.get_name()
replacements[p2_arg.get_name()] = token
p1_args[i].set_name(token)
p2_args[i].set_name(token)
continue
const = ''
var = ''
if p1_arg.is_constant() and p2_arg.is_variable():
const = p1_arg.get_name()
var = p2_arg.get_name()
else:
const = p2_arg.get_name()
var = p1_arg.get_name()
if '({0})'.format(const) in var: # can't to unification
return p1, p2, False
replacements[var] = const
p1_args[i].set_name(const)
p2_args[i].set_name(const)
p1._args = p1_args
p2._args = p2_args
return p1, p2, True
def resolution(l):
if len(l) == 1:
return False
setofSupport = list(l)
fgh = list(l)
sizeFgh = len(fgh)
l.sort(key = len)
for (x, y) in enumerate(l):
refSet = l[x]
setofSupport.remove(refSet)
newClause = addNewClause(refSet,setofSupport)
if newClause ==None:
return False
elif len(newClause) ==0:
return True
else:
if newClause not in fgh:
fgh.append(setofSupport)
newFghSize = len(fgh)
if newFghSize > sizeFgh:
resolution(fgh)
return False
def addNewClause(refSet,setofSupport):
newClause =[]
for (i, e) in enumerate(refSet):
setofSupport.sort(key=len)
for (j,k) in enumerate(setofSupport):
check = False
for(m,n) in enumerate(k):
if e.complement_of_predicate(n) or check == True:
check = True
reps = dict()
p1, p2, flag = unification(e, n, reps)
if flag == True:
n = p2