def reverse_premises(syllogism, first=True, second=True):
additional_premises = []
if first:
additional_premises.append(syllogism[0] + sylutil.term_order(syllogism[2])[0][::-1])
if second:
additional_premises.append(syllogism[1] + sylutil.term_order(syllogism[2])[1][::-1])
return additional_premises
def reencode(self, syllogism, vm, conclusions):
# sort rows (individuals) of VM by access time (most recent first)
sorted_inds = sorted(vm, key=lambda x: x.t, reverse=True)
# sort properties per individual by access time (most recent first), flatten and uniquify
sorted_props = [sorted(ind.props, key=lambda p: p.t, reverse=True) for ind in sorted_inds]
sorted_props = sylutil.uniquify_keep_order([p for l in sorted_props for p in l])
p1_terms, p2_terms = sylutil.term_order(syllogism[2])
for prop in sorted_props:
for target_premise in [syllogism[0] + p1_terms, syllogism[1] + p2_terms]:
if prop.name in target_premise:
# reencode the target premise without additional information
if not prop.neg:
vm = self.extend_vm(vm, target_premise, reencoding=True)
new_conclusions = self.conclude(vm)
if any([c not in conclusions for c in new_conclusions]):
return vm, new_conclusions
# get indirect information encoded as additional premise
prem, subj_neg = self.get_additional_premises(target_premise, prop)
if prem is not None:
# reencode using the additional premise
vm = self.extend_vm(vm, prem, reencoding=True, subj_neg=subj_neg)
new_conclusions = self.conclude(vm)
if any([c not in conclusions for c in new_conclusions]):
return vm, new_conclusions
return vm, ["NVC"]
def encode(self, syllogism):
""" Returns a VM by initially encoding a syllogism
>>> vm = VerbalModels()
>>> vm.params.update(dict.fromkeys(["p1", "p2", "p3", "p4", "p5", "p6"], "a"))
>>> vm.encode("IA4") # p. 539
[[b'(0), a(0), c(1)](0), [b'(0), c(1)](0)]
>>> vm.encode("IA3") # p. 542
[[a'(2), b(2)](2), [a'(2)](2), [c'(3), b(3)](3)]
>>> vm.encode("AI1") # p. 542
[[a'(4), b'(4), c(5)](5), [a'(4), b'(4)](5)]
>>> vm.encode("EI1") # own
[[a'(6), -b(6)](6), [b'(7), c(7)](7), [b'(7)](7)]
>>> vm.encode("AA1") # own
[[a'(8), b'(8), c(9)](8)]
>>> vm.encode("EE1") # own
[[a'(10), -b(10)](10), [b'(11), -c(11)](11)]
"""
vm = []
premises = [syllogism[i] + sylutil.term_order(syllogism[2])[i] for i in [0, 1]]
for premise in premises:
vm = self.extend_vm(vm, premise, reencoding=False)
return vm
def syllogism_combinations(syllogism, additional_premises):
"""
>>> syllogism_combinations("AA1", ["Aba"])
['AA4']
"""
for p in additional_premises:
if p[0] not in syllogism:
raise NotImplementedError
new_syllogisms = []
for p in additional_premises:
i = 0 if "a" in p and "b" in p else 1
i_other = (i + 1) % 2
premises = [None, None]
premises[i] = p
premises[i_other] = syllogism[i_other] + sylutil.term_order(
syllogism[2])[i_other]
if premises[0][1:] == "ab" and premises[1][1:] == "bc":
figure = "1"
elif premises[0][1:] == "ba" and premises[1][1:] == "cb":
figure = "2"
elif premises[0][1:] == "ab" and premises[1][1:] == "cb":
figure = "3"
elif premises[0][1:] == "ba" and premises[1][1:] == "bc":
figure = "4"
else:
raise Exception
new_syllogisms.append(premises[0][0] + premises[1][0] + figure)
return new_syllogisms
def search_counterexample(self, conclusion, syllogism):
""" Brute force search for counterexamples over generic models """
premises = [syllogism[i] + sylutil.term_order(syllogism[2])[i] for i in [0, 1]]
for generic_model in self.generic_models():
# only models that satisfy the premises can be valid counterexamples
if all([self.check_if_holds(generic_model, prem) for prem in premises]):
if not self.check_if_holds(generic_model, conclusion):
return generic_model
return None
def encode_premises(self,
syllogism,
ex_implicatures=True,
grice_implicatures=False):
""" Encode premises as propositions, possibly adding implicatures """
to = sylutil.term_order(syllogism[2])
premises = []
pr = []
for i in [0, 1]:
pr.append(syllogism[i] + to[i])
pr = sylutil.add_implicatures(pr,
existential=ex_implicatures,
gricean=grice_implicatures)
for p in pr:
premises.append(self.encode_proposition(p, True))
return premises
def encode(self, syllogism, size=4, deviation=0.0):
if size < 2:
size = 2
mm = []
(subj0, pred0), (subj1, pred1) = sylutil.term_order(syllogism[2])
### Encode first premise ###
# individuals that must be present in the model of the 1st premise
required_inds = {
"A": [[subj0, pred0]],
"I": [[subj0, pred0]],
"E": [[subj0, "-" + pred0], ["-" + subj0, pred0]],
"O": [[subj0, "-" + pred0]]
}[syllogism[0]]
appendix = []
# O needs an additional requirement to make sure "b" is present (otherwise e.g. [a -b] [-a -b] would be allowed)
while not all([ind in appendix for ind in required_inds]) or \
syllogism[0] == "O" and not any([prop == pred0 for ind in appendix for prop in ind]):
appendix = []
for i in range(size):
appendix.append(
self.draw_individual(syllogism[0], subj0, pred0,
random.random() < deviation))
mm.extend(appendix)
i_b = [i for i, row in enumerate(mm) if "b" in row]
### Encode second premise ###
if syllogism[1] == "A":
for i in i_b:
mm[i].append("c")
elif syllogism[1] == "I":
if subj1 == "b":
for n, i in enumerate(i_b):
mm[i].append("c")
if n == 1:
break
elif subj1 == "c":
mm[i_b[0]].append("c")
mm.extend([["c"]])
elif syllogism[1] == "E":
if subj1 == "b":
for i in i_b:
mm[i].append("-c")
mm.append(["c"])
elif subj1 == "c":
mm.extend([[subj1, "-" + pred1], [subj1, "-" + pred1],
[subj1, "-" + pred1], [subj1, "-" + pred1]])
elif syllogism[1] == "O":
if subj1 == "b":
for n, i in enumerate(i_b):
mm[i].append("-c")
# augment max 2 individuals
if n == 1:
break
mm.append(["c"])
elif subj1 == "c":
mm.extend([["-b", "c"], ["c"]])
return [sorted(row, key=lambda e: e[-1]) for row in mm]
def encode(self, syllogism):
""" Returns initial MM representation of a syllogism + list of exhausted terms
>>> mm = MentalModels()
>>> mm.encode("AA1")
([['a', 'b', 'c'], ['a', 'b', 'c']], ['a', 'b'])
>>> mm.encode("AA2")
([['a', 'b', 'c'], ['a', 'b', 'c']], ['b', 'c'])
>>> mm.encode("AA3")
([['a', 'b', 'c'], ['a', 'b', 'c']], ['a', 'c'])
>>> mm.encode("AA4")
([['a', 'b', 'c'], ['a', 'b', 'c']], ['b'])
>>> mm.encode("AE1")
([['a', 'b', '-c'], ['a', 'b', '-c'], ['c'], ['c']], ['a', 'b', 'c'])
>>> mm.encode("AE2")
([['a', 'b'], ['a', 'b'], ['-b', 'c'], ['-b', 'c']], ['b', 'c'])
>>> mm.encode("AE3")
([['a', 'b'], ['a', 'b'], ['-b', 'c'], ['-b', 'c']], ['a', 'b', 'c'])
>>> mm.encode("AE4")
([['a', 'b', '-c'], ['a', 'b', '-c'], ['c'], ['c']], ['b', 'c'])
>>> mm.encode("AI1")
([['a', 'b', 'c'], ['a', 'b'], ['c']], ['a'])
>>> mm.encode("AI2")
([['a', 'b', 'c'], ['a', 'b'], ['c']], ['b'])
>>> mm.encode("AI3")
([['a', 'b', 'c'], ['a', 'b'], ['c']], ['a'])
>>> mm.encode("AI4")
([['a', 'b', 'c'], ['a', 'b'], ['c']], ['b'])
>>> mm.encode("AO1")
([['a', 'b', '-c'], ['a', 'b', '-c'], ['c'], ['c']], ['a'])
>>> mm.encode("AO2")
([['a', 'b'], ['a', 'b'], ['-b', 'c'], ['-b', 'c']], ['b'])
>>> mm.encode("AO3")
([['a', 'b'], ['a', 'b'], ['-b', 'c'], ['-b', 'c']], ['a'])
>>> mm.encode("AO4")
([['a', 'b', '-c'], ['a', 'b', '-c'], ['c'], ['c']], ['b'])
>>> mm.encode("EA1")
([['a', '-b'], ['a', '-b'], ['b', 'c'], ['b', 'c']], ['a', 'b'])
>>> mm.encode("EA2")
([['-a', 'b', 'c'], ['-a', 'b', 'c'], ['a'], ['a']], ['a', 'b', 'c'])
>>> mm.encode("EA3")
([['a', '-b'], ['a', '-b'], ['b', 'c'], ['b', 'c']], ['a', 'b', 'c'])
>>> mm.encode("EI1")
([['a', '-b'], ['a', '-b'], ['b', 'c'], ['b'], ['c']], ['a', 'b'])
>>> mm.encode("EI3")
([['a', '-b'], ['a', '-b'], ['b', 'c'], ['b'], ['c']], ['a', 'b'])
>>> mm.encode("IA1")
([['a', 'b', 'c'], ['a'], ['b', 'c']], ['b'])
>>> mm.encode("IA3")
([['a', 'b', 'c'], ['a'], ['b', 'c']], ['c'])
>>> mm.encode("IA4")
([['a', 'b', 'c'], ['b', 'c'], ['a']], ['b'])
>>> mm.encode("IE1")
([['a', 'b', '-c'], ['a'], ['b', '-c'], ['c'], ['c']], ['b', 'c'])
>>> mm.encode("II1")
([['a', 'b', 'c'], ['a'], ['b'], ['c']], [])
>>> mm.encode("IO1")
([['a', 'b', '-c'], ['a'], ['b', '-c'], ['c'], ['c']], [])
>>> mm.encode("OA4")
([['-a', 'b', 'c'], ['-a', 'b', 'c'], ['a'], ['a']], ['b'])
>>> mm.encode("OE4")
([['-a', 'b', '-c'], ['-a', 'b', '-c'], ['a'], ['a'], ['c'], ['c']], ['b', 'c'])
>>> mm.encode("OI4")
([['-a', 'b', 'c'], ['-a', 'b'], ['a'], ['a'], ['c']], [])
"""
mm = []
exhausted = set()
to = sylutil.term_order(syllogism[2])
subj_0, pred_0 = to[0]
subj_1, pred_1 = to[1]
if syllogism[0] == "A":
mm.extend(([subj_0, pred_0], [subj_0, pred_0]))
exhausted.add(subj_0)
if syllogism[0] == "I":
mm.extend(([subj_0, pred_0], [subj_0], [pred_0]))
if syllogism[0] == "E":
mm.extend(([subj_0, "-" + pred_0], [subj_0, "-" + pred_0], [pred_0], [pred_0]))
exhausted.update((subj_0, pred_0))
if syllogism[0] == "O":
mm.extend(([subj_0, "-" + pred_0], [subj_0, "-" + pred_0], [pred_0], [pred_0]))
i_b = [i for i, row in enumerate(mm) if "b" in row]
if syllogism[1] == "A":
for i in i_b:
mm[i].append("c")
exhausted.add(subj_1)
if syllogism[1] == "I":
mm[i_b[0]].append("c")
mm.append(["c"])
if syllogism[1] == "E" or syllogism[1] == "O":
if subj_1 == "b":
for i in i_b:
mm[i].append("-c")
mm.extend((["c"], ["c"]))
else:
mm.extend((["-b", "c"], ["-b", "c"]))
if syllogism[1] == "E":
exhausted.update(("b", "c"))
return [sorted(row, key=lambda e: e[-1]) for row in mm], sorted(list(exhausted))
