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Logic_S5.py
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Logic_S5.py
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__author__ = 'marcincuber'
# -*- coding: utf-8 -*-
"""
:Modal Logic S5- symmetric, reflexive and transitive frames- equivalence relation
"""
import syntax
import sols
import graph as gr
import networkx as nx
import copy
from collections import OrderedDict
import time
#import symbols
SET = syntax.Language(*syntax.ascii_setup)
'''
:Arrays to store the number of worlds and sets that correspond to each world
'''
Graphs = [] #initilise empty list of graphs
Sets = [] #initilise list to store formulas which will be available in each world
graph_formulas = [] #list of dictionaries-used formulas in node for graph
formulas = {} #single dictionary
formulas[1] = [] #first list for node 1
graph_formulas.append(formulas)#add it to list of dictionaries
'''
:Input String:
'''
str_psi = "((~DDB~p V (~BDp ^ DDq)) > (D~BDs ^ D~Bt)) "
print "formula input: ", (str_psi)
'''
:Parsed string into tuple and list
'''
psi = syntax.parse_formula(SET, str_psi)
Sets.append(sols.recursivealpha(psi))
'''
:creating initial graph
'''
G = nx.MultiDiGraph()
uniq_Sets = [list(OrderedDict.fromkeys(l)) for l in Sets]
gr.create_graph_K(G,uniq_Sets)
Graphs.append(G)
'''
:functions to remove duplicates from the list
'''
def remove_duplicates(lista):
return list(set(lista))
def remove_dups_graph(graph):
for node in graph.nodes():
value_list = graph.node[node]
unique_list = remove_duplicates(value_list)
graph.node[node] = unique_list
'''
:resolving ALPHAS given a GRAPH
'''
def alpha_node(graph):
for node in graph.nodes():
set = []
value_list = graph.node[node]
for i in range(0,len(value_list)):
if isinstance(value_list[i], tuple):
alpha = sols.recursivealpha(value_list[i])
for j in alpha:
if isinstance(j, tuple):
if j not in set:
set.append(j)
else:
for prop in alpha:
set.append(prop)
elif isinstance(value_list[i], str):
set.append(value_list[i])
graph.node[node] = remove_duplicates(set)
'''
:resolving ALPHAS given a NODE in graph
'''
def alpha_node_solve(graph,node):
set = [] # array to store expanded alphas
value_list = graph.node[node]
for i in range(0,len(value_list)):
if isinstance(value_list[i], tuple):
alpha = sols.recursivealpha(value_list[i])
for j in alpha:
if isinstance(j, tuple):
if j not in set:
set.append(j)
else:
for prop in alpha:
if prop not in set:
set.append(prop)
elif isinstance(value_list[i], str):
if value_list[i] not in set:
set.append(value_list[i])
graph.node[node] = set
'''
:resolving BETAS given a NODE in graph
'''
def beta_node_solve(graph, node, formulas_in):
value_list = graph.node[node]
for i in range(0,len(value_list)):
value = value_list[i]
if value not in formulas_in[node]:
if value[0] =='or':
part1 = value[1]
part2 = value[2]
comp2 = graph.copy()
graph.node[node].remove(value)
comp2.node[node].remove(value)
graph.node[node].append(part1)
comp2.node[node].append(part2)
Graphs.append(comp2)
formulas_in[node].append(value)
copy_formulas_in = copy.deepcopy(formulas_in)
graph_formulas.append(copy_formulas_in)
for graph in Graphs:
alpha_node(graph)
elif value_list[i] == 'or':
part1 = value_list[i+1]
part2 = value_list[i+2]
comp2 = graph.copy()
graph.node[node] = []
comp2.node[node] = []
graph.node[node].append(part1)
comp2.node[node].append(part2)
Graphs.append(comp2)
formulas_in[node].append(value)
copy_formulas_in = copy.deepcopy(formulas_in)
graph_formulas.append(copy_formulas_in)
for graph in Graphs:
alpha_node(graph)
elif value[0] == 'not' and value[1][0] == 'and':
part1 = value[1][1]
part2 = value[1][2]
left_part = ('not',part1)
right_part = ('not',part2)
comp2 = graph.copy()
graph.node[node].remove(value)
comp2.node[node].remove(value)
graph.node[node].append(left_part)
comp2.node[node].append(right_part)
Graphs.append(comp2)
formulas_in[node].append(value)
copy_formulas_in = copy.deepcopy(formulas_in)
graph_formulas.append(copy_formulas_in)
for graph in Graphs:
alpha_node(graph)
elif value[0] == 'imply':
part1 = value[1]
part2 = value[2]
left_part = ('not',part1)
comp2 = graph.copy()
graph.node[node].remove(value)
comp2.node[node].remove(value)
graph.node[node].append(left_part)
comp2.node[node].append(part2)
Graphs.append(comp2)
formulas_in[node].append(value)
copy_formulas_in = copy.deepcopy(formulas_in)
graph_formulas.append(copy_formulas_in)
for graph in Graphs:
alpha_node(graph)
elif value_list[i] == 'imply':
part1 = value_list[i+1]
part2 = value_list[i+2]
left_part = ('not',part1)
comp2 = graph.copy()
graph.node[node] = []
comp2.node[node] = []
graph.node[node].append(left_part)
comp2.node[node].append(part2)
Graphs.append(comp2)
formulas_in.append(value)
copy_formulas_in = copy.deepcopy(formulas_in)
graph_formulas.append(copy_formulas_in)
for graph in Graphs:
alpha_node(graph)
'''
:resolving DELTAS given a NODE in graph
'''
def delta_node_solve(graph, node, formulas_in):
delta_list = graph.node[node]
for i in range(len(delta_list)-1,-1,-1):
part1 = delta_list[i][0]
if part1 == 'diamond':
sub = delta_list[i]
part2 = delta_list[i][1]
if (sub not in formulas_in[node]) and (part2 not in graph.node[node]):
formulas_in[node].append(sub)
status = False
for node_int in graph.nodes():
if (sub in formulas_in[node_int]) and (node != node_int):
status = True
break
if part2 in graph.node[node_int]:
status = True
break
if status == False:
new_node= graph.number_of_nodes()+1
graph.node[new_node] = [part2]
formulas_in[new_node] = []
alpha_node_solve(graph, node)
beta_node_solve(graph, node, formulas_in)
for single_node in graph.nodes():
if single_node != new_node:
set = graph.node[single_node]
for j in range(0,len(set)):
if set[j][0] == 'not' and set[j][1][0] == 'diamond' and set[j][1][1][0] == 'box':
pass
elif set[j][0] == 'box' and set[j][1][0] == 'diamond':
pass
elif set[j][0] == 'not' and set[j][1][0] == 'diamond':
formula = ('not',set[j][1][1])
if formula not in graph.node[new_node]:
graph.node[new_node].append(formula)
alpha_node_solve(graph, new_node)
beta_node_solve(graph, new_node, formulas_in)
elif set[j][0] == 'box':
if set[j][1] not in graph.node[new_node]:
graph.node[new_node].append(set[j][1])
alpha_node_solve(graph, new_node)
beta_node_solve(graph, new_node, formulas_in)
elif part1 == 'not' and delta_list[i][1][0] == 'box':
sub = delta_list[i]
part2 = ('not', delta_list[i][1][1])
if (sub not in formulas_in[node]) and (part2 not in graph.node[node]):
formulas_in[node].append(sub)
status = False
for node_int in graph.nodes():
if (sub in formulas_in[node_int]) and (node != node_int):
status = True
break
if part2 in graph.node[node_int]:
status = True
break
if status == False:
new_node= graph.number_of_nodes()+1
graph.node[new_node] = [part2]
formulas_in[new_node] = []
alpha_node_solve(graph, node)
beta_node_solve(graph, node, formulas_in)
for single_node in graph.nodes():
if single_node != new_node:
set = graph.node[single_node]
for j in range(0,len(set)):
if set[j][0] == 'not' and set[j][1][0] == 'diamond' and set[j][1][1][0] == 'box':
pass
elif set[j][0] == 'box' and set[j][1][0] == 'diamond':
pass
elif set[j][0] == 'not' and set[j][1][0] == 'diamond':
formula = ('not',set[j][1][1])
if formula not in graph.node[new_node]:
graph.node[new_node].append(formula)
alpha_node_solve(graph, new_node)
beta_node_solve(graph, new_node, formulas_in)
elif set[j][0] == 'box':
if set[j][1] not in graph.node[new_node]:
graph.node[new_node].append(set[j][1])
alpha_node_solve(graph, new_node)
beta_node_solve(graph, new_node, formulas_in)
'''
:solving gammas at a NODE in graph
'''
def gamma_node_solve(graph, node, formulas_in):
value_list = graph.node[node]
size = len(graph.node[node])
status = 1;
index = 0;
while status == 1:
for i in range(index,size):
value = value_list[i]
if value[0] == 'box':
formula = value[1]
if value not in formulas_in[node]:
formulas_in[node].append(value)
if value[0] == 'box' and value[1][0] == "diamond":
value_list.remove(value)
graph.node[node]= value_list
if formula not in graph.node[node]:
graph.node[node].append(formula)
else:
for single_node in graph.nodes():
if formula not in graph.node[single_node]:
graph.node[single_node].append(formula)
elif value[0] == 'not' and value[1][0] == "diamond":
formula = ('not', value[1][1])
if value not in formulas_in[node]:
formulas_in[node].append(value)
if value[0] == 'not' and value[1][0] == "diamond" and value[1][1][0] == 'box':
value_list.remove(value)
graph.node[node]= value_list
formula = ('not',value[1][1])
if formula not in graph.node[node]:
graph.node[node].append(formula)
else:
for single_node in graph.nodes():
if formula not in graph.node[single_node]:
graph.node[single_node].append(formula)
new_size = len(graph.node[node])
if size == new_size:
status = 0;
else:
diff = new_size - size
index = len(graph.node[node])-diff
size = new_size
""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""
""" Main loop iterating over graphs """
""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""
def main():
num_graph = 0
for graph in Graphs:
formulas_in = graph_formulas[num_graph]
status = 1;
index = 1;
alpha_node(graph)
while status == 1:
for node in range(index,len(graph.nodes())+1):
start_length = len(graph.nodes())
alpha_node_solve(graph,node)
beta_node_solve(graph, node,formulas_in)
gamma_node_solve(graph, node, formulas_in)
delta_node_solve(graph, node,formulas_in)
alpha_node_solve(graph,node)
beta_node_solve(graph, node,formulas_in)
gamma_node_solve(graph, node, formulas_in)
delta_node_solve(graph, node, formulas_in)
end_length = len(graph.nodes())
if start_length < end_length:
diff = end_length - start_length
index = index+1
elif index < len(graph.nodes()):
index = index+1
else:
status = 0;
num_graph += 1
'''
:finding inconsistencies in the model
'''
index_inconsistent =[]
for i in range(0,len(Graphs)):
graph = Graphs[i]
for node in graph.nodes():
consistent_list = graph.node[node]
status = sols.inconsistent(consistent_list)
if status == True:
index_inconsistent.append(i)
else:
status == False
index_inconsistent = list(set(index_inconsistent))
# removing inconsistent graphs- models
if index_inconsistent is not []:
for num in reversed(index_inconsistent):
del Graphs[num];
'''
:display and save as pictures all the exiting graphs in the list
'''
gr.final_graphs(Graphs,psi)
t0 = time.clock()
main()
print ((time.clock() - t0), " seconds process time")