def dpll_satisfiable(expr):
"""
Check satisfiability of a propositional sentence.
It returns a model rather than True when it succeeds
>>> from diofant.abc import A, B
>>> from diofant.logic.algorithms.dpll import dpll_satisfiable
>>> dpll_satisfiable(A & ~B) == {A: True, B: False}
True
>>> dpll_satisfiable(A & ~A)
False
"""
clauses = conjuncts(to_cnf(expr))
if False in clauses:
return False
symbols = sorted(_find_predicates(expr), key=default_sort_key)
symbols_int_repr = set(range(1, len(symbols) + 1))
clauses_int_repr = to_int_repr(clauses, symbols)
result = dpll_int_repr(clauses_int_repr, symbols_int_repr, {})
if not result:
return result
output = {}
for key in result:
output.update({symbols[key - 1]: result[key]})
return output
def dpll_satisfiable(expr, all_models=False):
"""
Check satisfiability of a propositional sentence.
It returns a model rather than True when it succeeds.
Returns a generator of all models if all_models is True.
Examples
========
>>> from diofant.abc import A, B
>>> from diofant.logic.algorithms.dpll2 import dpll_satisfiable
>>> dpll_satisfiable(A & ~B) == {A: True, B: False}
True
>>> dpll_satisfiable(A & ~A)
False
"""
clauses = conjuncts(to_cnf(expr))
if False in clauses:
if all_models:
return (f for f in [False])
return False
symbols = sorted(_find_predicates(expr), key=default_sort_key)
symbols_int_repr = range(1, len(symbols) + 1)
clauses_int_repr = to_int_repr(clauses, symbols)
solver = SATSolver(clauses_int_repr, symbols_int_repr, set(), symbols)
models = solver._find_model()
if all_models:
return _all_models(models)
try:
return next(models)
except StopIteration:
return False
def test_to_cnf():
assert to_cnf(~(B | C)) == And(Not(B), Not(C))
assert to_cnf((A & B) | C) == And(Or(A, C), Or(B, C))
assert to_cnf(A >> B) == (~A) | B
assert to_cnf(A >> (B & C)) == (~A | B) & (~A | C)
assert to_cnf(A & (B | C) | ~A & (B | C), True) == B | C
assert to_cnf(Equivalent(A, B)) == And(Or(A, Not(B)), Or(B, Not(A)))
assert to_cnf(Equivalent(A, B & C)) == \
(~A | B) & (~A | C) & (~B | ~C | A)
assert to_cnf(Equivalent(A, B | C), True) == \
And(Or(Not(B), A), Or(Not(C), A), Or(B, C, Not(A)))
assert to_cnf(~(A | B) | C) == And(Or(Not(A), C), Or(Not(B), C))
def satisfiable(expr, algorithm="dpll2", all_models=False):
"""
Check satisfiability of a propositional sentence.
Returns a model when it succeeds.
Returns {true: true} for trivially true expressions.
On setting all_models to True, if given expr is satisfiable then
returns a generator of models. However, if expr is unsatisfiable
then returns a generator containing the single element False.
Examples
========
>>> from diofant.abc import A, B
>>> from diofant.logic.inference import satisfiable
>>> satisfiable(A & ~B) == {A: True, B: False}
True
>>> satisfiable(A & ~A)
False
>>> satisfiable(True)
{true: True}
>>> next(satisfiable(A & ~A, all_models=True))
False
>>> models = satisfiable((A >> B) & B, all_models=True)
>>> next(models) == {A: False, B: True}
True
>>> next(models) == {A: True, B: True}
True
>>> def use_models(models):
... for model in models:
... if model:
... # Do something with the model.
... return model
... else:
... # Given expr is unsatisfiable.
... print("UNSAT")
>>> use_models(satisfiable(A >> ~A, all_models=True))
{A: False}
>>> use_models(satisfiable(A ^ A, all_models=True))
UNSAT
"""
expr = to_cnf(expr)
if algorithm == "dpll":
from diofant.logic.algorithms.dpll import dpll_satisfiable
return dpll_satisfiable(expr)
elif algorithm == "dpll2":
from diofant.logic.algorithms.dpll2 import dpll_satisfiable
return dpll_satisfiable(expr, all_models)
else: # pragma: no cover
raise NotImplementedError
def retract(self, sentence):
"""Remove the sentence's clauses from the KB
Examples
========
>>> from diofant.logic.inference import PropKB
>>> from diofant.abc import x, y
>>> l = PropKB()
>>> l.clauses
[]
>>> l.tell(x | y)
>>> l.clauses
[Or(x, y)]
>>> l.retract(x | y)
>>> l.clauses
[]
"""
for c in conjuncts(to_cnf(sentence)):
self.clauses_.discard(c)
def tell(self, sentence):
"""Add the sentence's clauses to the KB
Examples
========
>>> from diofant.logic.inference import PropKB
>>> from diofant.abc import x, y
>>> l = PropKB()
>>> l.clauses
[]
>>> l.tell(x | y)
>>> l.clauses
[Or(x, y)]
>>> l.tell(y)
>>> l.clauses
[y, Or(x, y)]
"""
for c in conjuncts(to_cnf(sentence)):
self.clauses_.add(c)