o *ήc^!@sdZddlmZmZmZmZmZddlmZddl m Z ddl m Z ddZ dd d Zd d ZdddZdddZGdddZGdddeZdS)z Inference in propositional logic)AndNot conjunctsto_cnfBooleanFunction)ordered)sympify) import_modulec CsV|dus|dur |Sz|jr|WS|jrt|jdWStttfy*tdw)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.) is_Symbolis_Notliteral_symbolargs ValueErrorAttributeError)literalr>> 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 Npycosatzpycosat module is not presentdpll2 minisat22pysatdpllr)dpll_satisfiable)pycosat_satisfiable)minisat22_satisfiable) r ImportErrorsympy.logic.algorithms.dpllrsympy.logic.algorithms.dpll2&sympy.logic.algorithms.pycosat_wrapperr(sympy.logic.algorithms.minisat22_wrapperrNotImplementedError) expr algorithm all_modelsminimalrrrrrrrr satisfiable&s0*       r%cCstt| S)ax 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] https://en.wikipedia.org/wiki/Validity )r%rr!rrrvalidosr'csddlmdfdd|vr|St|}|s$td||s(i}fdd|D}||}|vr@t|S|r^d d|D}t||rXt |rVd Sd St |s^d Sd S) a+ Returns whether the given assignment is a model or not. If the assignment does not specify the value for every proposition, this may return None to indicate 'not obvious'. Parameters ========== model : dict, optional, default: {} Mapping of symbols to boolean values to indicate assignment. deep: boolean, optional, default: False Gives the value of the expression under partial assignments correctly. May still return None to indicate 'not obvious'. Examples ======== >>> from sympy.abc import A, B >>> from sympy.logic.inference import pl_true >>> pl_true( A & B, {A: True, B: True}) True >>> pl_true(A & B, {A: False}) False >>> pl_true(A & B, {A: True}) >>> pl_true(A & B, {A: True}, deep=True) >>> pl_true(A >> (B >> A)) >>> pl_true(A >> (B >> A), deep=True) True >>> pl_true(A & ~A) >>> pl_true(A & ~A, deep=True) False >>> pl_true(A & B & (~A | ~B), {A: True}) >>> pl_true(A & B & (~A | ~B), {A: True}, deep=True) False r)Symbol)TFcs<t|s |vr dSt|tsdStfdd|jDS)NTFc3s|]}|VqdSNr).0arg) _validaterr sz-pl_true.._validate..) isinstancerallr r&r(r,booleanrrr,s  zpl_true.._validatez$%s is not a valid boolean expressioncsi|] \}}|vr||qSrr)r*kv)r1rr szpl_true..cSsi|]}|dqS)Tr)r*r2rrrr4sTFN) sympy.core.symbolr(rritemssubsboolatomspl_truer'r%)r!modeldeepresultrr0rr:s. (   r:cCs.|rt|}ng}|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] https://en.wikipedia.org/wiki/Logical_consequence )listappendrr%r)r! formula_setrrrentailss  rAc@s>eZdZdZd ddZddZddZd d Zed d Z dS)KBz"Base class for all knowledge basesNcCst|_|r ||dSdSr))setclauses_tellselfsentencerrr__init__sz KB.__init__cCtr)r rFrrrrEzKB.tellcCrJr)rKrGqueryrrraskrLzKB.askcCrJr)rKrFrrrretractrLz KB.retractcCstt|jSr))r>rrD)rGrrrclausessz KB.clausesr)) __name__ __module__ __qualname____doc__rIrErOrPpropertyrQrrrrrBs rBc@s(eZdZdZddZddZddZdS) PropKBz=A KB for Propositional Logic. Inefficient, with no indexing.cC"tt|D]}|j|qdS)aiAdd 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)rrrDaddrGrHcrrrrE z PropKB.tellcCs t||jS)a8Checks 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 )rArDrMrrrrO!s z PropKB.askcCrX)amRemove 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)rrrDdiscardrZrrrrP3r\zPropKB.retractN)rRrSrTrUrErOrPrrrrrWs  rW)NFF)NFr))rUsympy.logic.boolalgrrrrrsympy.core.sortingrsympy.core.sympifyrsympy.external.importtoolsr r r%r'r:rArBrWrrrrs    I  I!