Ed^!dZddlmZmZmZmZmZddlmZddl m Z ddl m Z dZ dd Zd Zdd Zdd ZGd dZGddeZdS)z Inference in propositional logic)AndNot conjunctsto_cnfBooleanFunction)ordered)sympify) import_modulec|dus|dur|S |jr|S|jrt|jdSt#t tf$rt dwxYw)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)literals 5lib/python3.11/site-packages/sympy/logic/inference.pyrr s $'U*@   N > !',q/22 2  J '@@@>???@s= ==!ANFch||dkr+td}|d}n|dkrtdd}|dkrtd}|d}|dkrdd lm}||S|dkrdd lm}|||S|dkrdd lm}|||S|dkrdd lm}||||St) 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 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_modelsminimalrrrrrs r satisfiabler'&sRT  I2   **  !III% C!"ABBB I+ g&&  IF @@@@@@@%%% g @AAAAAAj111 i @NNNNNN""4444 k !@RRRRRR$$T:w??? c<tt| 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'r)r#s rvalidr*os*3t99%% %%r(cddlmdfd|vr|St|}|std|z|si}fd|D}||}|vrt |S|rQd|D}t||rt|rdSnt|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)TFct|s|vrdSt|tsdStfd|jDS)NTFc3.K|]}|VdSN).0arg _validates r z-pl_true.._validate..s+77c99S>>777777r() isinstancerallr)r#r,r3booleans rr3zpl_true.._validatesa dF # # tw 4$00 57777TY777777r(z$%s is not a valid boolean expressionc$i|] \}}|v || Sr0r0)r1kvr7s r zpl_true..s( < < .s111QD111r(TFN) sympy.core.symbolr,r ritemssubsboolatomspl_truer*r')r#modeldeepresultr,r3r7s @@@rrBrBsFP)(((((G8888888 w 4==D 9T??H?$FGGG  < < < >> 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_sets rentailsrJsP2;''  s4yy!!!3 ,-- --r(cBeZdZdZddZdZdZdZedZ dS) KBz"Base class for all knowledge basesNc^t|_|r||dSdSr/)setclauses_tellselfsentences r__init__z KB.__init__s7  IIh       r(ctr/r"rQs rrPzKB.tell!!r(ctr/rVrRquerys raskzKB.askrWr(ctr/rVrQs rretractz KB.retractrWr(cDtt|jSr/)rGrrO)rRs rclausesz KB.clausessGDM**+++r(r/) __name__ __module__ __qualname____doc__rTrPr[r]propertyr_r0r(rrLrLsv,,    """"""""",,X,,,r(rLc$eZdZdZdZdZdZdS)PropKBz=A KB for Propositional Logic. Inefficient, with no indexing.cxtt|D]}|j|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)rrrOaddrRrScs rrPz PropKB.tell sF*6(++,, ! !A M  a  ! !r(c,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 )rJrOrYs rr[z PropKB.ask!s udm,,,r(cxtt|D]}|j|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)rrrOdiscardris rr]zPropKB.retract3sF*6(++,, % %A M ! !! $ $ $ $ % %r(N)r`rarbrcrPr[r]r0r(rrfrfsGGG!!!0---$%%%%%r(rf)NFF)NFr/)rcsympy.logic.boolalgrrrrrsympy.core.sortingrsympy.core.sympifyr sympy.external.importtoolsr rr'r*rBrJrLrfr0r(rrrs9&&LLLLLLLLLLLLLL&&&&&&&&&&&&444444@@@:FFFFR&&&0FFFFR....B,,,,,,,,*C%C%C%C%C%RC%C%C%C%C%r(