o Ïe^!ã@s”dZddlmZmZmZmZmZddlmZddl m Z ddl m Z dd„Z dd d „Zd d „Zddd„Zddd„ZGdd„dƒZGdd„deƒZdS)z Inference in propositional logicé)ÚAndÚNotÚ conjunctsÚto_cnfÚBooleanFunction)Úordered)Úsympify)Ú import_modulec CsV|dus|dur |Sz|jr|WS|jrt|jdƒWSt‚ttfy*tdƒ‚w)zó 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.)Z is_SymbolZis_NotÚliteral_symbolÚargsÚ ValueErrorÚAttributeError)Úliteral©rúED:\Projects\ConvertPro\env\Lib\site-packages\sympy/logic/inference.pyr sÿr NFc CsÒ|dus|dkrtdƒ}|durd}n |dkrtdƒ‚d}|dkr+tdƒ}|dur+d}|dkr9dd lm}||ƒS|dkrHdd lm}|||ƒS|dkrWdd lm}|||ƒS|dkrgdd lm}||||ƒSt ‚) aÚ 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 NÚpycosatzpycosat module is not presentZdpll2Z minisat22ÚpysatZdpllr)Údpll_satisfiable)Úpycosat_satisfiable)Úminisat22_satisfiable) r Ú ImportErrorZsympy.logic.algorithms.dpllrZsympy.logic.algorithms.dpll2Z&sympy.logic.algorithms.pycosat_wrapperrZ(sympy.logic.algorithms.minisat22_wrapperrÚNotImplementedError) ÚexprÚ algorithmZ all_modelsZminimalrrrrrrrrÚ satisfiable&s0*       rcCstt|ƒƒ 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 )rr©rrrrÚvalidosrcsÀddlm‰d‰‡‡‡fdd„‰|ˆvr|St|ƒ}ˆ|ƒs$td|ƒ‚|s(i}‡fdd„| ¡Dƒ}| |¡}|ˆvr@t|ƒS|r^d d„| ¡Dƒ}t||ƒrXt |ƒrVd Sd St |ƒs^d Sd S) a+ Returns whether the given assignment is a model or not. If the assignment does not specify the value for every proposition, this may return None to indicate 'not obvious'. Parameters ========== model : dict, optional, default: {} Mapping of symbols to boolean values to indicate assignment. deep: boolean, optional, default: False Gives the value of the expression under partial assignments correctly. May still return None to indicate 'not obvious'. Examples ======== >>> from sympy.abc import A, B >>> from sympy.logic.inference import pl_true >>> pl_true( A & B, {A: True, B: True}) True >>> pl_true(A & B, {A: False}) False >>> pl_true(A & B, {A: True}) >>> pl_true(A & B, {A: True}, deep=True) >>> pl_true(A >> (B >> A)) >>> pl_true(A >> (B >> A), deep=True) True >>> pl_true(A & ~A) >>> pl_true(A & ~A, deep=True) False >>> pl_true(A & B & (~A | ~B), {A: True}) >>> pl_true(A & B & (~A | ~B), {A: True}, deep=True) False r)ÚSymbol)TFcs<t|ˆƒs |ˆvr dSt|tƒsdSt‡fdd„|jDƒƒS)NTFc3s|]}ˆ|ƒVqdS©Nr)Ú.0Úarg)Ú _validaterrÚ ¸s€z-pl_true.._validate..)Ú isinstancerÚallr r©rr!Úbooleanrrr!³s  zpl_true.._validatez$%s is not a valid boolean expressioncsi|] \}}|ˆvr||“qSrr)rÚkÚv)r&rrÚ Ászpl_true..cSsi|]}|d“qS)Tr)rr'rrrr)ÆsTFN) Zsympy.core.symbolrrr ÚitemsÚsubsÚboolZatomsÚpl_truerr)rÚmodelÚdeepÚresultrr%rr-‡s. (   þr-cCs.|rt|ƒ}ng}| t|ƒ¡tt|Žƒ S)aø 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 )ÚlistÚappendrrr)rZ formula_setrrrÚentailsÐs  r3c@s>eZdZdZd dd„Zdd„Zdd„Zd d „Zed d „ƒZ dS)ÚKBz"Base class for all knowledge basesNcCstƒ|_|r | |¡dSdSr)ÚsetÚclauses_Útell©ÚselfÚsentencerrrÚ__init__ósÿz KB.__init__cCót‚r©rr8rrrr7øózKB.tellcCr<rr=©r9ÚqueryrrrÚaskûr>zKB.askcCr<rr=r8rrrÚretractþr>z KB.retractcCstt|jƒƒSr)r1rr6)r9rrrÚclausessz KB.clausesr) Ú__name__Ú __module__Ú __qualname__Ú__doc__r;r7rArBÚpropertyrCrrrrr4ñs r4c@s(eZdZdZdd„Zdd„Zdd„ZdS) ÚPropKBz=A KB for Propositional Logic. Inefficient, with no indexing.cCó"tt|ƒƒD]}|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)rrr6Úadd©r9r:Úcrrrr7 óÿz PropKB.tellcCs t||jƒS)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 )r3r6r?rrrrA!s z PropKB.askcCrJ)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)rrr6ÚdiscardrLrrrrB3rNzPropKB.retractN)rDrErFrGr7rArBrrrrrIs  rI)NFF)NFr)rGZsympy.logic.boolalgrrrrrZsympy.core.sortingrZsympy.core.sympifyrZsympy.external.importtoolsr r rrr-r3r4rIrrrrÚs    I  I!