U L?h#@sdZddlmZmZmZmZmZddlmZddl m Z ddl m Z ddZ dd d Zd d ZdddZdddZGdddZGdddeZdS)z Inference in propositional logic)AndNot conjunctsto_cnfBooleanFunction)ordered)sympify) import_modulecCs>|dks|dkr|S|jr|S|jr2t|jdStddS)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 ValueError)literalrG/var/www/html/venv/lib/python3.8/site-packages/sympy/logic/inference.pyr sr NFc Cs@|r(|dk r$|dkr$td|dd}|dks8|dkrbtd}|dk rNd}n|dkr^tdd}|dkr~td}|dkr~d}|d krtd }|dkrd}|d krd d lm}||S|dkrd d lm}||||d S|dkrd dlm} | ||S|dkrd dlm } | |||S|d kr8d dl m } | ||St dS)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 NZdpll2z2Currently only dpll2 can handle using lra theory. z is not handled.pycosatzpycosat module is not presentZ minisat22pysatz3Zdpllr)dpll_satisfiable)use_lra_theory)pycosat_satisfiable)minisat22_satisfiable)z3_satisfiable) r r ImportErrorZsympy.logic.algorithms.dpllrZsympy.logic.algorithms.dpll2Z&sympy.logic.algorithms.pycosat_wrapperrZ(sympy.logic.algorithms.minisat22_wrapperrZ!sympy.logic.algorithms.z3_wrapperrNotImplementedError) expr algorithmZ all_modelsZminimalrrrrrrrrrrr satisfiable#sF*          rcCstt| 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 )rrrrrrvalidzsrcsddlmdfdd|kr,|St|}|sHtd||sPi}fdd|D}||}|krt|S|rt| 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 >>> 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|krdSt|ts$dStfdd|jDS)NTFc3s|]}|VqdSNr).0arg) _validaterr sz-pl_true.._validate..) isinstancerallr rrr#booleanrrr#s  zpl_true.._validatez$%s is not a valid boolean expressioncsi|]\}}|kr||qSrr)r!kv)r(rr szpl_true..TFN) Zsympy.core.symbolrrr itemssubsbooldictfromkeysZatomspl_truerr)rmodeldeepresultrr'rr1s,(    r1cCs.|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 )listappendrrr)rZ formula_setrrrentailss  r7c@s>eZdZdZd ddZddZddZd d Zed d Z dS)KBz"Base class for all knowledge basesNcCst|_|r||dSr )setclauses_tellselfsentencerrr__init__sz KB.__init__cCstdSr rr<rrrr;szKB.tellcCstdSr r@r=queryrrraskszKB.askcCstdSr r@r<rrrretract sz KB.retractcCstt|jSr )r5rr:)r=rrrclauses sz KB.clauses)N) __name__ __module__ __qualname____doc__r?r;rCrDpropertyrErrrrr8s r8c@s(eZdZdZddZddZddZdS) PropKBz=A KB for Propositional Logic. Inefficient, with no indexing.cCs"tt|D]}|j|q dS)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)rrr:addr=r>crrrr;sz 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 )r7r:rArrrrC,sz PropKB.askcCs"tt|D]}|j|q dS)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)rrr:discardrMrrrrD>szPropKB.retractN)rFrGrHrIr;rCrDrrrrrKsrK)NFFF)NF)N)rIZsympy.logic.boolalgrrrrrZsympy.core.sortingrZsympy.core.sympifyrZsympy.external.importtoolsr r rrr1r7r8rKrrrrs    W I !