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