B [@sdZddlmZmZddlmZmZmZmZddl m Z ddl m Z ddZ dd d Zd d Zid fddZifddZGdddeZGdddeZdS)z Inference in propositional logic)print_functiondivision)AndNot conjunctsto_cnf)ordered)sympifyc Cs`|dks|dkr|Sy&|jr |S|jr4t|jdStWn ttfk rZtdYnXdS)z The symbol in this literal (without the negation). Examples ======== >>> from sympy.abc import A >>> from sympy.logic.inference import literal_symbol >>> literal_symbol(A) A >>> literal_symbol(~A) A TFrz#Argument must be a boolean literal.N)Z is_SymbolZis_Notliteral_symbolargs ValueErrorAttributeError)literalr4lib/python3.7/site-packages/sympy/logic/inference.pyr sr dpll2FcCsJt|}|dkr$ddlm}||S|dkrBddlm}|||StdS)a 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 sympy.abc import A, B >>> from sympy.logic.inference import satisfiable >>> satisfiable(A & ~B) {A: True, B: False} >>> 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} >>> next(models) {A: True, B: True} >>> def use_models(models): ... for model in models: ... if model: ... # Do something with the model. ... print(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 Zdpllr)dpll_satisfiablerN)rZsympy.logic.algorithms.dpllrZsympy.logic.algorithms.dpll2NotImplementedError)expr algorithmZ all_modelsrrrr satisfiable&s*   rcCstt| S)aw Check validity of a propositional sentence. A valid propositional sentence is True under every assignment. Examples ======== >>> from sympy.abc import A, B >>> from sympy.logic.inference import valid >>> valid(A | ~A) True >>> valid(A | B) False References ========== .. [1] http://en.wikipedia.org/wiki/Validity )rr)rrrrvalidZsrcsddlmddlmdfdd|kr:|St|}|sVtd|tfdd |D}||}|krt |S|rtd d | D}t ||rt |rd Sn t |sd Sd S)a- Returns whether the given assignment is a model or not. If the assignment does not specify the value for every proposition, this may return None to indicate 'not obvious'. Parameters ========== model : dict, optional, default: {} Mapping of symbols to boolean values to indicate assignment. deep: boolean, optional, default: False Gives the value of the expression under partial assignments correctly. May still return None to indicate 'not obvious'. Examples ======== >>> from sympy.abc import A, B, C >>> from sympy.logic.inference import pl_true >>> pl_true( A & B, {A: True, B: True}) True >>> pl_true(A & B, {A: False}) False >>> pl_true(A & B, {A: True}) >>> pl_true(A & B, {A: True}, deep=True) >>> pl_true(A >> (B >> A)) >>> pl_true(A >> (B >> A), deep=True) True >>> pl_true(A & ~A) >>> pl_true(A & ~A, deep=True) False >>> pl_true(A & B & (~A | ~B), {A: True}) >>> pl_true(A & B & (~A | ~B), {A: True}, deep=True) False r)Symbol)BooleanFunction)TFcs<t|s|krdSt|s$dStfdd|jDS)NTFc3s|]}|VqdS)Nr).0arg) _validaterr sz-pl_true.._validate..) isinstanceallr )r)rrrbooleanrrrs  zpl_true.._validatez$%s is not a valid boolean expressionc3s"|]\}}|kr||fVqdS)Nr)rkv)r rrrszpl_true..css|]}|dfVqdS)TNr)rr!rrrrsTFN)Zsympy.core.symbolrsympy.logic.boolalgrr r dictitemsZsubsboolZatomspl_truerr)rZmodelZdeepresultr)rrrr rr'rs*'     r'cCs$t|}|t|tt| S)a Check whether the given expr_set entail an expr. If formula_set is empty then it returns the validity of expr. Examples ======== >>> from sympy.abc import A, B, C >>> from sympy.logic.inference import entails >>> entails(A, [A >> B, B >> C]) False >>> entails(C, [A >> B, B >> C, A]) True >>> entails(A >> B) False >>> entails(A >> (B >> A)) True References ========== .. [1] http://en.wikipedia.org/wiki/Logical_consequence )listappendrrr)rZ formula_setrrrentailssr+c@s>eZdZdZd ddZddZddZd d Zed d Z dS)KBz"Base class for all knowledge basesNcCst|_|r||dS)N)setclauses_tell)selfsentencerrr__init__sz KB.__init__cCstdS)N)r)r0r1rrrr/szKB.tellcCstdS)N)r)r0queryrrraskszKB.askcCstdS)N)r)r0r1rrrretractsz KB.retractcCstt|jS)N)r)rr.)r0rrrclausessz KB.clauses)N) __name__ __module__ __qualname____doc__r2r/r4r5propertyr6rrrrr,s  r,c@s(eZdZdZddZddZddZdS) PropKBz=A KB for Propositional Logic. Inefficient, with no indexing.cCs&x tt|D]}|j|qWdS)ahAdd the sentence's clauses to the KB Examples ======== >>> from sympy.logic.inference import PropKB >>> from sympy.abc import x, y >>> l = PropKB() >>> l.clauses [] >>> l.tell(x | y) >>> l.clauses [x | y] >>> l.tell(y) >>> l.clauses [y, x | y] N)rrr.add)r0r1crrrr/sz PropKB.tellcCs t||jS)a7Checks if the query is true given the set of clauses. Examples ======== >>> from sympy.logic.inference import PropKB >>> from sympy.abc import x, y >>> l = PropKB() >>> l.tell(x & ~y) >>> l.ask(x) True >>> l.ask(y) False )r+r.)r0r3rrrr4sz PropKB.askcCs&x tt|D]}|j|qWdS)alRemove the sentence's clauses from the KB Examples ======== >>> from sympy.logic.inference import PropKB >>> from sympy.abc import x, y >>> l = PropKB() >>> l.clauses [] >>> l.tell(x | y) >>> l.clauses [x | y] >>> l.retract(x | y) >>> l.clauses [] N)rrr.discard)r0r1r>rrrr5szPropKB.retractN)r7r8r9r:r/r4r5rrrrr<sr<N)rF)r:Z __future__rrr#rrrrZsympy.core.compatibilityrZsympy.core.sympifyr r rrr'r+objectr,r<rrrrs   4F