def unique_names_demo():
lexpr = Expression.fromstring
p1 = lexpr(r"man(Socrates)")
p2 = lexpr(r"man(Bill)")
c = lexpr(r"exists x.exists y.(x != y)")
prover = Prover9Command(c, [p1, p2])
print(prover.prove())
unp = UniqueNamesProver(prover)
print("assumptions:")
for a in unp.assumptions():
print(" ", a)
print("goal:", unp.goal())
print(unp.prove())
p1 = lexpr(r"all x.(walk(x) -> (x = Socrates))")
p2 = lexpr(r"Bill = William")
p3 = lexpr(r"Bill = Billy")
c = lexpr(r"-walk(William)")
prover = Prover9Command(c, [p1, p2, p3])
print(prover.prove())
unp = UniqueNamesProver(prover)
print("assumptions:")
for a in unp.assumptions():
print(" ", a)
print("goal:", unp.goal())
print(unp.prove())
def unique_names_demo():
lexpr = Expression.fromstring
p1 = lexpr(r'man(Socrates)')
p2 = lexpr(r'man(Bill)')
c = lexpr(r'exists x.exists y.(x != y)')
prover = Prover9Command(c, [p1, p2])
print(prover.prove())
unp = UniqueNamesProver(prover)
print('assumptions:')
for a in unp.assumptions():
print(' ', a)
print('goal:', unp.goal())
print(unp.prove())
p1 = lexpr(r'all x.(walk(x) -> (x = Socrates))')
p2 = lexpr(r'Bill = William')
p3 = lexpr(r'Bill = Billy')
c = lexpr(r'-walk(William)')
prover = Prover9Command(c, [p1, p2, p3])
print(prover.prove())
unp = UniqueNamesProver(prover)
print('assumptions:')
for a in unp.assumptions():
print(' ', a)
print('goal:', unp.goal())
print(unp.prove())
def add_sentence(self, sentence, informchk=False, consistchk=False):
"""
Add a sentence to the current discourse.
Updates ``self._input`` and ``self._sentences``.
:param sentence: An input sentence
:type sentence: str
:param informchk: if ``True``, check that the result of adding the sentence is thread-informative. Updates ``self._readings``.
:param consistchk: if ``True``, check that the result of adding the sentence is thread-consistent. Updates ``self._readings``.
"""
# check whether the new sentence is informative (i.e. not entailed by the previous discourse)
if informchk:
self.readings(verbose=False)
for tid in sorted(self._threads):
assumptions = [
reading for (rid, reading) in self.expand_threads(tid)
]
assumptions += self._background
for sent_reading in self._get_readings(sentence):
tp = Prover9Command(goal=sent_reading,
assumptions=assumptions)
if tp.prove():
print("Sentence '%s' under reading '%s':" %
(sentence, str(sent_reading)))
print("Not informative relative to thread '%s'" % tid)
self._input.append(sentence)
self._sentences = dict([("s%s" % i, sent)
for i, sent in enumerate(self._input)])
# check whether adding the new sentence to the discourse preserves consistency (i.e. a model can be found for the combined set of
# of assumptions
if consistchk:
self.readings(verbose=False)
self.models(show=False)
def default_reasoning_demo():
lexpr = Expression.fromstring
premises = []
#define taxonomy
premises.append(lexpr(r'all x.(elephant(x) -> animal(x))'))
premises.append(lexpr(r'all x.(bird(x) -> animal(x))'))
premises.append(lexpr(r'all x.(dove(x) -> bird(x))'))
premises.append(lexpr(r'all x.(ostrich(x) -> bird(x))'))
premises.append(lexpr(r'all x.(flying_ostrich(x) -> ostrich(x))'))
#default properties
premises.append(lexpr(r'all x.((animal(x) & -Ab1(x)) -> -fly(x))')) #normal animals don't fly
premises.append(lexpr(r'all x.((bird(x) & -Ab2(x)) -> fly(x))')) #normal birds fly
premises.append(lexpr(r'all x.((ostrich(x) & -Ab3(x)) -> -fly(x))')) #normal ostriches don't fly
#specify abnormal entities
premises.append(lexpr(r'all x.(bird(x) -> Ab1(x))')) #flight
premises.append(lexpr(r'all x.(ostrich(x) -> Ab2(x))')) #non-flying bird
premises.append(lexpr(r'all x.(flying_ostrich(x) -> Ab3(x))')) #flying ostrich
#define entities
premises.append(lexpr(r'elephant(E)'))
premises.append(lexpr(r'dove(D)'))
premises.append(lexpr(r'ostrich(O)'))
#print the assumptions
prover = Prover9Command(None, premises)
command = UniqueNamesProver(ClosedWorldProver(prover))
for a in command.assumptions(): print(a)
print_proof('-fly(E)', premises)
print_proof('fly(D)', premises)
print_proof('-fly(O)', premises)
def closed_world_demo():
lexpr = Expression.fromstring
p1 = lexpr(r"walk(Socrates)")
p2 = lexpr(r"(Socrates != Bill)")
c = lexpr(r"-walk(Bill)")
prover = Prover9Command(c, [p1, p2])
print(prover.prove())
cwp = ClosedWorldProver(prover)
print("assumptions:")
for a in cwp.assumptions():
print(" ", a)
print("goal:", cwp.goal())
print(cwp.prove())
p1 = lexpr(r"see(Socrates, John)")
p2 = lexpr(r"see(John, Mary)")
p3 = lexpr(r"(Socrates != John)")
p4 = lexpr(r"(John != Mary)")
c = lexpr(r"-see(Socrates, Mary)")
prover = Prover9Command(c, [p1, p2, p3, p4])
print(prover.prove())
cwp = ClosedWorldProver(prover)
print("assumptions:")
for a in cwp.assumptions():
print(" ", a)
print("goal:", cwp.goal())
print(cwp.prove())
p1 = lexpr(r"all x.(ostrich(x) -> bird(x))")
p2 = lexpr(r"bird(Tweety)")
p3 = lexpr(r"-ostrich(Sam)")
p4 = lexpr(r"Sam != Tweety")
c = lexpr(r"-bird(Sam)")
prover = Prover9Command(c, [p1, p2, p3, p4])
print(prover.prove())
cwp = ClosedWorldProver(prover)
print("assumptions:")
for a in cwp.assumptions():
print(" ", a)
print("goal:", cwp.goal())
print(cwp.prove())
def closed_world_demo():
lexpr = Expression.fromstring
p1 = lexpr(r'walk(Socrates)')
p2 = lexpr(r'(Socrates != Bill)')
c = lexpr(r'-walk(Bill)')
prover = Prover9Command(c, [p1, p2])
print(prover.prove())
cwp = ClosedWorldProver(prover)
print('assumptions:')
for a in cwp.assumptions():
print(' ', a)
print('goal:', cwp.goal())
print(cwp.prove())
p1 = lexpr(r'see(Socrates, John)')
p2 = lexpr(r'see(John, Mary)')
p3 = lexpr(r'(Socrates != John)')
p4 = lexpr(r'(John != Mary)')
c = lexpr(r'-see(Socrates, Mary)')
prover = Prover9Command(c, [p1, p2, p3, p4])
print(prover.prove())
cwp = ClosedWorldProver(prover)
print('assumptions:')
for a in cwp.assumptions():
print(' ', a)
print('goal:', cwp.goal())
print(cwp.prove())
p1 = lexpr(r'all x.(ostrich(x) -> bird(x))')
p2 = lexpr(r'bird(Tweety)')
p3 = lexpr(r'-ostrich(Sam)')
p4 = lexpr(r'Sam != Tweety')
c = lexpr(r'-bird(Sam)')
prover = Prover9Command(c, [p1, p2, p3, p4])
print(prover.prove())
cwp = ClosedWorldProver(prover)
print('assumptions:')
for a in cwp.assumptions():
print(' ', a)
print('goal:', cwp.goal())
print(cwp.prove())
def combination_prover_demo():
lexpr = Expression.fromstring
p1 = lexpr(r"see(Socrates, John)")
p2 = lexpr(r"see(John, Mary)")
c = lexpr(r"-see(Socrates, Mary)")
prover = Prover9Command(c, [p1, p2])
print(prover.prove())
command = ClosedDomainProver(UniqueNamesProver(ClosedWorldProver(prover)))
for a in command.assumptions():
print(a)
print(command.prove())
def combination_prover_demo():
lp = LogicParser()
p1 = lp.parse(r'see(Socrates, John)')
p2 = lp.parse(r'see(John, Mary)')
c = lp.parse(r'-see(Socrates, Mary)')
prover = Prover9Command(c, [p1, p2])
print(prover.prove())
command = ClosedDomainProver(UniqueNamesProver(ClosedWorldProver(prover)))
for a in command.assumptions():
print(a)
print(command.prove())
def print_proof(goal, premises):
lexpr = Expression.fromstring
prover = Prover9Command(lexpr(goal), premises)
command = UniqueNamesProver(ClosedWorldProver(prover))
print(goal, prover.prove(), command.prove())
def closed_domain_demo():
lexpr = Expression.fromstring
p1 = lexpr(r"exists x.walk(x)")
p2 = lexpr(r"man(Socrates)")
c = lexpr(r"walk(Socrates)")
prover = Prover9Command(c, [p1, p2])
print(prover.prove())
cdp = ClosedDomainProver(prover)
print("assumptions:")
for a in cdp.assumptions():
print(" ", a)
print("goal:", cdp.goal())
print(cdp.prove())
p1 = lexpr(r"exists x.walk(x)")
p2 = lexpr(r"man(Socrates)")
p3 = lexpr(r"-walk(Bill)")
c = lexpr(r"walk(Socrates)")
prover = Prover9Command(c, [p1, p2, p3])
print(prover.prove())
cdp = ClosedDomainProver(prover)
print("assumptions:")
for a in cdp.assumptions():
print(" ", a)
print("goal:", cdp.goal())
print(cdp.prove())
p1 = lexpr(r"exists x.walk(x)")
p2 = lexpr(r"man(Socrates)")
p3 = lexpr(r"-walk(Bill)")
c = lexpr(r"walk(Socrates)")
prover = Prover9Command(c, [p1, p2, p3])
print(prover.prove())
cdp = ClosedDomainProver(prover)
print("assumptions:")
for a in cdp.assumptions():
print(" ", a)
print("goal:", cdp.goal())
print(cdp.prove())
p1 = lexpr(r"walk(Socrates)")
p2 = lexpr(r"walk(Bill)")
c = lexpr(r"all x.walk(x)")
prover = Prover9Command(c, [p1, p2])
print(prover.prove())
cdp = ClosedDomainProver(prover)
print("assumptions:")
for a in cdp.assumptions():
print(" ", a)
print("goal:", cdp.goal())
print(cdp.prove())
p1 = lexpr(r"girl(mary)")
p2 = lexpr(r"dog(rover)")
p3 = lexpr(r"all x.(girl(x) -> -dog(x))")
p4 = lexpr(r"all x.(dog(x) -> -girl(x))")
p5 = lexpr(r"chase(mary, rover)")
c = lexpr(r"exists y.(dog(y) & all x.(girl(x) -> chase(x,y)))")
prover = Prover9Command(c, [p1, p2, p3, p4, p5])
print(prover.prove())
cdp = ClosedDomainProver(prover)
print("assumptions:")
for a in cdp.assumptions():
print(" ", a)
print("goal:", cdp.goal())
print(cdp.prove())
def closed_domain_demo():
lexpr = Expression.fromstring
p1 = lexpr(r'exists x.walk(x)')
p2 = lexpr(r'man(Socrates)')
c = lexpr(r'walk(Socrates)')
prover = Prover9Command(c, [p1, p2])
print(prover.prove())
cdp = ClosedDomainProver(prover)
print('assumptions:')
for a in cdp.assumptions():
print(' ', a)
print('goal:', cdp.goal())
print(cdp.prove())
p1 = lexpr(r'exists x.walk(x)')
p2 = lexpr(r'man(Socrates)')
p3 = lexpr(r'-walk(Bill)')
c = lexpr(r'walk(Socrates)')
prover = Prover9Command(c, [p1, p2, p3])
print(prover.prove())
cdp = ClosedDomainProver(prover)
print('assumptions:')
for a in cdp.assumptions():
print(' ', a)
print('goal:', cdp.goal())
print(cdp.prove())
p1 = lexpr(r'exists x.walk(x)')
p2 = lexpr(r'man(Socrates)')
p3 = lexpr(r'-walk(Bill)')
c = lexpr(r'walk(Socrates)')
prover = Prover9Command(c, [p1, p2, p3])
print(prover.prove())
cdp = ClosedDomainProver(prover)
print('assumptions:')
for a in cdp.assumptions():
print(' ', a)
print('goal:', cdp.goal())
print(cdp.prove())
p1 = lexpr(r'walk(Socrates)')
p2 = lexpr(r'walk(Bill)')
c = lexpr(r'all x.walk(x)')
prover = Prover9Command(c, [p1, p2])
print(prover.prove())
cdp = ClosedDomainProver(prover)
print('assumptions:')
for a in cdp.assumptions():
print(' ', a)
print('goal:', cdp.goal())
print(cdp.prove())
p1 = lexpr(r'girl(mary)')
p2 = lexpr(r'dog(rover)')
p3 = lexpr(r'all x.(girl(x) -> -dog(x))')
p4 = lexpr(r'all x.(dog(x) -> -girl(x))')
p5 = lexpr(r'chase(mary, rover)')
c = lexpr(r'exists y.(dog(y) & all x.(girl(x) -> chase(x,y)))')
prover = Prover9Command(c, [p1, p2, p3, p4, p5])
print(prover.prove())
cdp = ClosedDomainProver(prover)
print('assumptions:')
for a in cdp.assumptions():
print(' ', a)
print('goal:', cdp.goal())
print(cdp.prove())
def print_proof(goal, premises):
lp = LogicParser()
prover = Prover9Command(lp.parse(goal), premises)
command = UniqueNamesProver(ClosedWorldProver(prover))
print(goal, prover.prove(), command.prove())
