def test_literal():
A, B = symbols('A,B')
assert is_literal(True) is True
assert is_literal(False) is True
assert is_literal(A) is True
assert is_literal(~A) is True
assert is_literal(Or(A, B)) is False
assert literal_symbol(True) is True
assert literal_symbol(False) is False
assert literal_symbol(A) is A
assert literal_symbol(~A) is A
def find_unit_clause(clauses, model):
"""A unit clause has only 1 variable that is not bound in the model.
>>> from sympy import symbols
>>> A, B, C = symbols('ABC')
>>> find_unit_clause([A | B | C, B | ~C, A | ~B], {A:True})
(B, False)
"""
for clause in clauses:
num_not_in_model = 0
for literal in disjuncts(clause):
sym = literal_symbol(literal)
if sym not in model:
num_not_in_model += 1
P, value = sym, not (isinstance(literal, Not))
if num_not_in_model == 1:
return P, value
return None, None
def find_unit_clause(clauses, model):
"""
A unit clause has only 1 variable that is not bound in the model.
>>> from sympy import symbols
>>> from sympy.abc import A, B, D
>>> from sympy.logic.algorithms.dpll import find_unit_clause
>>> find_unit_clause([A | B | D, B | ~D, A | ~B], {A:True})
(B, False)
"""
for clause in clauses:
num_not_in_model = 0
for literal in disjuncts(clause):
sym = literal_symbol(literal)
if sym not in model:
num_not_in_model += 1
P, value = sym, not (literal.func is Not)
if num_not_in_model == 1:
return P, value
return None, None
def find_unit_clause(clauses, model):
"""
A unit clause has only 1 variable that is not bound in the model.
>>> from sympy import symbols
>>> from sympy.abc import A, B, D
>>> from sympy.logic.algorithms.dpll import find_unit_clause
>>> find_unit_clause([A | B | D, B | ~D, A | ~B], {A:True})
(B, False)
"""
for clause in clauses:
num_not_in_model = 0
for literal in disjuncts(clause):
sym = literal_symbol(literal)
if sym not in model:
num_not_in_model += 1
P, value = sym, not isinstance(literal, Not)
if num_not_in_model == 1:
return P, value
return None, None
def ask(expr, key, assumptions=True):
"""
Method for inferring properties about objects.
**Syntax**
* ask(expression, key)
* ask(expression, key, assumptions)
where expression is any SymPy expression
**Examples**
>>> from sympy import ask, Q, Assume, pi
>>> from sympy.abc import x, y
>>> ask(pi, Q.rational)
False
>>> ask(x*y, Q.even, Assume(x, Q.even) & Assume(y, Q.integer))
True
>>> ask(x*y, Q.prime, Assume(x, Q.integer) & Assume(y, Q.integer))
False
**Remarks**
Relations in assumptions are not implemented (yet), so the following
will not give a meaningful result.
>> ask(x, positive=True, Assume(x>0))
It is however a work in progress and should be available before
the official release
"""
expr = sympify(expr)
assumptions = And(assumptions, And(*global_assumptions))
# direct resolution method, no logic
resolutors = []
for handler in handlers_dict[key]:
resolutors.append( get_class(handler) )
res, _res = None, None
mro = inspect.getmro(type(expr))
for handler in resolutors:
for subclass in mro:
if hasattr(handler, subclass.__name__):
res = getattr(handler, subclass.__name__)(expr, assumptions)
if _res is None: _res = res
elif res is None:
# since first resolutor was conclusive, we keep that value
res = _res
else:
# only check consistency if both resolutors have concluded
if _res != res: raise ValueError, 'incompatible resolutors'
break
if res is not None:
return res
if assumptions is True: return
# use logic inference
if not expr.is_Atom: return
clauses = copy.deepcopy(known_facts_compiled)
assumptions = conjuncts(to_cnf(assumptions))
# add assumptions to the knowledge base
for assump in assumptions:
conj = eliminate_assume(assump, symbol=expr)
if conj:
out = []
for sym in conjuncts(to_cnf(conj)):
lit, pos = literal_symbol(sym), type(sym) is not Not
if pos:
out.extend([known_facts_keys.index(str(l))+1 for l in disjuncts(lit)])
else:
out.extend([-(known_facts_keys.index(str(l))+1) for l in disjuncts(lit)])
clauses.append(out)
n = len(known_facts_keys)
clauses.append([known_facts_keys.index(key)+1])
if not dpll_int_repr(clauses, range(1, n+1), {}):
return False
clauses[-1][0] = -clauses[-1][0]
if not dpll_int_repr(clauses, range(1, n+1), {}):
# if the negation is satisfiable, it is entailed
return True
del clauses
def test_literal():
A, B = symbols('A,B')
assert literal_symbol(True) is True
assert literal_symbol(False) is False
assert literal_symbol(A) is A
assert literal_symbol(~A) is A
def ask(expr, key, assumptions=True):
"""
Method for inferring properties about objects.
**Syntax**
* ask(expression, key)
* ask(expression, key, assumptions)
where expression is any SymPy expression
**Examples**
>>> from sympy import ask, Q, Assume, pi
>>> from sympy.abc import x, y
>>> ask(pi, Q.rational)
False
>>> ask(x*y, Q.even, Assume(x, Q.even) & Assume(y, Q.integer))
True
>>> ask(x*y, Q.prime, Assume(x, Q.integer) & Assume(y, Q.integer))
False
**Remarks**
Relations in assumptions are not implemented (yet), so the following
will not give a meaningful result.
>> ask(x, positive=True, Assume(x>0))
It is however a work in progress and should be available before
the official release
"""
expr = sympify(expr)
if type(key) is not Predicate:
key = getattr(Q, str(key))
assumptions = And(assumptions, And(*global_assumptions))
# direct resolution method, no logic
res = eval_predicate(key, expr, assumptions)
if res is not None:
return res
# use logic inference
if assumptions is True:
return
if not expr.is_Atom:
return
clauses = copy.deepcopy(known_facts_compiled)
assumptions = conjuncts(to_cnf(assumptions))
# add assumptions to the knowledge base
for assump in assumptions:
conj = eliminate_assume(assump, symbol=expr)
if conj:
for clause in conjuncts(to_cnf(conj)):
out = set()
for atom in disjuncts(clause):
lit, pos = literal_symbol(atom), type(atom) is not Not
if pos:
out.add(known_facts_keys.index(lit)+1)
else:
out.add(-(known_facts_keys.index(lit)+1))
clauses.append(out)
n = len(known_facts_keys)
clauses.append(set([known_facts_keys.index(key)+1]))
if not dpll_int_repr(clauses, set(range(1, n+1)), {}):
return False
clauses[-1] = set([-(known_facts_keys.index(key)+1)])
if not dpll_int_repr(clauses, set(range(1, n+1)), {}):
# if the negation is satisfiable, it is entailed
return True
del clauses
def ask(expr, key, assumptions=True):
"""
Method for inferring properties about objects.
**Syntax**
* ask(expression, key)
* ask(expression, key, assumptions)
where expression is any SymPy expression
**Examples**
>>> from sympy import ask, Q, Assume, pi
>>> from sympy.abc import x, y
>>> ask(pi, Q.rational)
False
>>> ask(x*y, Q.even, Assume(x, Q.even) & Assume(y, Q.integer))
True
>>> ask(x*y, Q.prime, Assume(x, Q.integer) & Assume(y, Q.integer))
False
**Remarks**
Relations in assumptions are not implemented (yet), so the following
will not give a meaningful result.
>> ask(x, positive=True, Assume(x>0))
It is however a work in progress and should be available before
the official release
"""
expr = sympify(expr)
assumptions = And(assumptions, And(*global_assumptions))
# direct resolution method, no logic
resolutors = []
for handler in handlers_dict[key]:
resolutors.append(get_class(handler))
res, _res = None, None
mro = inspect.getmro(type(expr))
for handler in resolutors:
for subclass in mro:
if hasattr(handler, subclass.__name__):
res = getattr(handler, subclass.__name__)(expr, assumptions)
if _res is None:
_res = res
elif res is None:
# since first resolutor was conclusive, we keep that value
res = _res
else:
# only check consistency if both resolutors have concluded
if _res != res:
raise ValueError('incompatible resolutors')
break
if res is not None:
return res
if assumptions is True:
return
# use logic inference
if not expr.is_Atom:
return
clauses = copy.deepcopy(known_facts_compiled)
assumptions = conjuncts(to_cnf(assumptions))
# add assumptions to the knowledge base
for assump in assumptions:
conj = eliminate_assume(assump, symbol=expr)
if conj:
out = set()
for sym in conjuncts(to_cnf(conj)):
lit, pos = literal_symbol(sym), type(sym) is not Not
if pos:
out.update([
known_facts_keys.index(str(l)) + 1
for l in disjuncts(lit)
])
else:
out.update([
-(known_facts_keys.index(str(l)) + 1)
for l in disjuncts(lit)
])
clauses.append(out)
n = len(known_facts_keys)
clauses.append(set([known_facts_keys.index(key) + 1]))
if not dpll_int_repr(clauses, set(range(1, n + 1)), {}):
return False
clauses[-1] = set([-(known_facts_keys.index(key) + 1)])
if not dpll_int_repr(clauses, set(range(1, n + 1)), {}):
# if the negation is satisfiable, it is entailed
return True
del clauses
