-
-
Notifications
You must be signed in to change notification settings - Fork 1
/
Logic_KB.py
558 lines (498 loc) · 24.9 KB
/
Logic_KB.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
__author__ = 'marcincuber'
# -*- coding: utf-8 -*-
"""
:Modal Logic KB- symmetric frames
"""
import syntax
import sols
import graph
import networkx as nx
import matplotlib.pyplot as plt
import copy
import time
from collections import OrderedDict
#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 = "(~B~Dp ^ DBDq) ^ B~s "
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]
graph.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]
if part1[0] == 'not':
left_part = part1[1]
else:
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]
if sub not in formulas_in[node]:
formulas_in[node].append(sub)
part2 = delta_list[i][1]
new_node= graph.number_of_nodes()+1
graph.add_edge(node,(new_node)) #adding new world and relation Rxx'
graph.add_edge((new_node), node) #add symmetric edge
graph.node[node] = delta_list
graph.node[new_node] = [part2]
formulas_in[new_node] = []
alpha_node_solve(graph, node)
beta_node_solve(graph, node, formulas_in)
previous = graph.predecessors(new_node)
for num in previous:
set = graph.node[num];
for j in range(0,len(set)):
if 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]
if sub not in formulas_in[node]:
formulas_in[node].append(sub)
part2 = ('not', delta_list[i][1][1])
new_node= graph.number_of_nodes()+1
graph.add_edge(node,(new_node)) #adding new world and relation Rxx'
graph.add_edge((new_node), node) #add symmetric edge
graph.node[node] = delta_list
graph.node[new_node] = [part2]
formulas_in[new_node] = []
alpha_node_solve(graph, node)
beta_node_solve(graph, node, formulas_in)
previous = graph.predecessors(new_node)
for num in previous:
set = graph.node[num];
for j in range(0,len(set)):
if 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 symmetric_gamma_node(graph, node, formulas_in):
value_list = graph.node[node]
size = len(value_list)
index = 0
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)
try:
graph.successors(node)
except:
break
next_node = graph.successors(node)
for single_node in next_node:
if single_node < node:
#take the initial size of list to check whether it expanded
initial_size = len(graph.node[single_node])
if formula not in graph.node[single_node]:
graph.node[single_node].append(formula)
alpha_node_solve(graph,single_node)
beta_node_solve(graph,single_node, formulas_in)
final_size = len(graph.node[single_node])
#take diff to scan for these new entries
diff_size = final_size-initial_size
if diff_size > 0:
value_list_single_node_initial= graph.node[single_node]
value_list_single_node = value_list_single_node_initial[-diff_size:]
for value in value_list_single_node:
if isinstance(value,tuple) and value[0] == 'box':
part = value[1]
if part not in graph.node[node]:
graph.node[node].append(part)
elif isinstance(value,tuple) and value[0] == 'not' and value[1][0] == 'diamond':
part = ('not',value[1][1])
if part not in graph.node[node]:
graph.node[node].append(part)
elif isinstance(value, tuple) and value[0] == 'diamond':
part = value[1]
new_node= graph.number_of_nodes()+1
#adding new world
graph.add_edge(single_node,(new_node))
#adding symmetric edge
graph.add_edge((new_node),single_node)
formulas_in[new_node] = []
graph.node[single_node] = value_list_single_node_initial
graph.node[new_node] = [part]
#expand new delta formulae
previous = graph.predecessors(new_node)
for num in previous:
set = graph.node[num];
for j in range(0,len(set)):
if 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 isinstance(value,tuple) and value[0] == 'not' and value[1][0] == 'box':
part = ('not', value[1][1])
new_node= graph.number_of_nodes()+1
#adding new world
graph.add_edge(single_node,(new_node))
#adding symmetric edge
graph.add_edge((new_node),single_node)
formulas_in[new_node] = []
graph.node[single_node] = value_list_single_node_initial
graph.node[new_node] = [part]
previous = graph.predecessors(new_node)
for num in previous:
set = graph.node[num];
for j in range(0,len(set)):
if 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)
alpha_node_solve(graph, node)
beta_node_solve(graph, node, formulas_in)
delta_node_solve(graph, node, formulas_in)
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)
try:
graph.successors(node)
except:
break
next_node = graph.successors(node)
for single_node in next_node:
if single_node < node:
#take the initial size of list to check whether it expanded
initial_size = len(graph.node[single_node])
if formula not in graph.node[single_node]:
graph.node[single_node].append(formula)
alpha_node_solve(graph, single_node)
beta_node_solve(graph, single_node, formulas_in)
final_size = len(graph.node[single_node])
#take diff to scan for these new entries
diff_size = final_size-initial_size
if diff_size > 0:
value_list_single_node_initial= graph.node[single_node]
value_list_single_node = value_list_single_node_initial[-diff_size:]
for value in value_list_single_node:
if isinstance(value,tuple) and value[0] == 'box':
part = value[1]
if part not in graph.node[node]:
graph.node[node].append(part)
elif isinstance(value,tuple) and value[0] == 'not' and value[1][0] == 'diamond':
part = ('not',value[1][1])
if part not in graph.node[node]:
graph.node[node].append(part)
elif isinstance(value, tuple) and value[0] == 'diamond':
part = value[1]
new_node= graph.number_of_nodes()+1
#adding new world
graph.add_edge(single_node,(new_node))
#adding symmetric edge
graph.add_edge((new_node),single_node)
formulas_in[new_node] = []
graph.node[single_node] = value_list_single_node_initial
graph.node[new_node] = [part]
previous = graph.predecessors(new_node)
for num in previous:
set = graph.node[num];
for j in range(0,len(set)):
if 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][0] 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 isinstance(value,tuple) and value[0] == 'not' and value[1][0] == 'box':
part = ('not', value[1][1])
new_node= graph.number_of_nodes()+1
#adding new world
graph.add_edge(single_node,(new_node))
#adding symmetric edge
graph.add_edge((new_node),single_node)
formulas_in[new_node] = []
graph.node[single_node] = value_list_single_node_initial
graph.node[new_node] = [part]
previous = graph.predecessors(new_node)
for num in previous:
set = graph.node[num];
for j in range(0,len(set)):
if 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][0] 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)
alpha_node_solve(graph, node)
beta_node_solve(graph, node, formulas_in)
delta_node_solve(graph, node, formulas_in)
""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""
""" 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)
delta_node_solve(graph, node, formulas_in)
symmetric_gamma_node(graph, node, formulas_in)
delta_node_solve(graph, node, formulas_in)
alpha_node_solve(graph,node)
beta_node_solve(graph, node, formulas_in)
delta_node_solve(graph, node, formulas_in)
symmetric_gamma_node(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
'''
if Graphs == []:
print "There are no models for the input formula: ", (syntax.formula_to_string(psi))
print "So the the negation of it : ", "~(",(syntax.formula_to_string(psi)), ") is valid."
else:
for i in range(0,len(Graphs)):
graph = Graphs[i]
custom_labels={}
node_colours=['y']
for node in graph.nodes():
custom_labels[node] = graph.node[node]
node_colours.append('c')
nx.draw(Graphs[i], nx.spring_layout(Graphs[i]), node_size=1500, with_labels=True, labels = custom_labels, node_color=node_colours)
#show with custom labels
fig_name = "graph" + str(i) + ".png"
plt.savefig(fig_name)
plt.show()
print "Satisfiable models have been displayed."
if len(Graphs) == 1:
print "You have ",len(Graphs), " valid model."
else:
print "You have ",len(Graphs), " valid models."
print "Your provided formula is: ", (syntax.formula_to_string(psi))
print "Pictures of the graphs have been saves as: graph0.png, graph1.png etc."
t0 = time.clock()
main()
print ((time.clock() - t0), " seconds process time")