ó ¡¼™\c@ sÊdZddlmZmZddlmZmZmZmZddl m Z ddl m Z d„Z ded„Zd „Zied „Zid „Zd efd „ƒYZdefd„ƒYZdS(s Inference in propositional logiciÿÿÿÿ(tprint_functiontdivision(tAndtNott conjunctstto_cnf(tordered(tsympifycC sw|tks|tkr|Sy1|jr,|S|jrFt|jdƒSt‚Wn#ttfk rrtdƒ‚nXdS(só 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 is#Argument must be a boolean literal.N(tTruetFalset is_Symboltis_Nottliteral_symboltargst ValueErrortAttributeError(tliteral((s4lib/python2.7/site-packages/sympy/logic/inference.pyR s   tdpll2cC set|ƒ}|dkr2ddlm}||ƒS|dkr[ddlm}|||ƒSt‚dS(sÚ 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 tdplliÿÿÿÿ(tdpll_satisfiableRN(Rtsympy.logic.algorithms.dpllRtsympy.logic.algorithms.dpll2tNotImplementedError(texprt algorithmt all_modelsR((s4lib/python2.7/site-packages/sympy/logic/inference.pyt satisfiable&s*     cC stt|ƒƒ S(sx 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(R((s4lib/python2.7/site-packages/sympy/logic/inference.pytvalidZsc s!ddlm‰ddlm‰ttf‰‡‡‡‡fd†‰|ˆkrT|St|ƒ}ˆ|ƒstd|ƒ‚nt‡fd†|j ƒDƒƒ}|j |ƒ}|ˆkrÆt |ƒS|rtd„|j ƒDƒƒ}t ||ƒr t|ƒrtSqt|ƒstSndS( s- 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 iÿÿÿÿ(tSymbol(tBooleanFunctionc sOt|ˆƒs|ˆkrtSt|ˆƒs2tSt‡fd†|jDƒƒS(Nc3 s|]}ˆ|ƒVqdS(N((t.0targ(t _validate(s4lib/python2.7/site-packages/sympy/logic/inference.pys ¢s(t isinstanceRR tallR (R(RRR tboolean(s4lib/python2.7/site-packages/sympy/logic/inference.pyR s s$%s is not a valid boolean expressionc3 s-|]#\}}|ˆkr||fVqdS(N((Rtktv(R#(s4lib/python2.7/site-packages/sympy/logic/inference.pys ©scs s|]}|tfVqdS(N(R(RR$((s4lib/python2.7/site-packages/sympy/logic/inference.pys ®sN(tsympy.core.symbolRtsympy.logic.boolalgRRR RRtdicttitemstsubstbooltatomstpl_trueRRtNone(Rtmodeltdeeptresult((RRR R#s4lib/python2.7/site-packages/sympy/logic/inference.pyR-rs*'    "    cC s0t|ƒ}|jt|ƒƒtt|Œƒ S(sø 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 (tlisttappendRRR(Rt formula_set((s4lib/python2.7/site-packages/sympy/logic/inference.pytentails¸s tKBcB sDeZdZdd„Zd„Zd„Zd„Zed„ƒZ RS(s"Base class for all knowledge basescC s&tƒ|_|r"|j|ƒndS(N(tsettclauses_ttell(tselftsentence((s4lib/python2.7/site-packages/sympy/logic/inference.pyt__init__Øs cC s t‚dS(N(R(R:R;((s4lib/python2.7/site-packages/sympy/logic/inference.pyR9ÝscC s t‚dS(N(R(R:tquery((s4lib/python2.7/site-packages/sympy/logic/inference.pytaskàscC s t‚dS(N(R(R:R;((s4lib/python2.7/site-packages/sympy/logic/inference.pytretractãscC stt|jƒƒS(N(R2RR8(R:((s4lib/python2.7/site-packages/sympy/logic/inference.pytclausesæsN( t__name__t __module__t__doc__R.R<R9R>R?tpropertyR@(((s4lib/python2.7/site-packages/sympy/logic/inference.pyR6Ös     tPropKBcB s)eZdZd„Zd„Zd„ZRS(s=A KB for Propositional Logic. Inefficient, with no indexing.cC s1x*tt|ƒƒD]}|jj|ƒqWdS(shAdd 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(RRR8tadd(R:R;tc((s4lib/python2.7/site-packages/sympy/logic/inference.pyR9îscC st||jƒS(s7Checks 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 (R5R8(R:R=((s4lib/python2.7/site-packages/sympy/logic/inference.pyR>scC s1x*tt|ƒƒD]}|jj|ƒqWdS(slRemove 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(RRR8tdiscard(R:R;RG((s4lib/python2.7/site-packages/sympy/logic/inference.pyR?s(RARBRCR9R>R?(((s4lib/python2.7/site-packages/sympy/logic/inference.pyREës  N(RCt __future__RRR'RRRRtsympy.core.compatibilityRtsympy.core.sympifyRR R RRR-R5tobjectR6RE(((s4lib/python2.7/site-packages/sympy/logic/inference.pyts" 4 F