\h#SrSSKJrJrJrJrJr SSKJr SSK J r SSK J r Sr SSjrS rSS jrSS jr"S S 5r"SS\5rg)z Inference in propositional logic)AndNot conjunctsto_cnfBooleanFunction)ordered)sympify) import_modulecUSLdUSLaU$UR(aU$UR(a[URS5$[ S5e)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 ValueError)literals M/var/www/auris/envauris/lib/python3.13/site-packages/sympy/logic/inference.pyrr sK $'U*    gll1o..>??NcU(aUbUS:wa[SUS35eSnUbUS:Xa$[S5nUbSnOUS:Xa [S5eSnUS:Xa[S5nUcSnUS:Xa[S5nUcSnUS :XaS S KJn U"U5$US:Xa S S KJn U"XUS 9$US:XaS S KJn U "X5$US:XaS SKJ n U "XU5$US:XaS SK J n U "X5$[e)aJ Check satisfiability of a propositional sentence. Returns a model when it succeeds. Returns {true: true} for trivially true expressions. On setting all_models to True, if given expr is satisfiable then returns a generator of models. However, if expr is unsatisfiable then returns a generator containing the single element False. Examples ======== >>> from sympy.abc import A, B >>> from sympy.logic.inference import satisfiable >>> satisfiable(A & ~B) {A: True, B: False} >>> satisfiable(A & ~A) False >>> satisfiable(True) {True: True} >>> next(satisfiable(A & ~A, all_models=True)) False >>> models = satisfiable((A >> B) & B, all_models=True) >>> next(models) {A: False, B: True} >>> next(models) {A: True, B: True} >>> def use_models(models): ... for model in models: ... if model: ... # Do something with the model. ... print(model) ... else: ... # Given expr is unsatisfiable. ... print("UNSAT") >>> use_models(satisfiable(A >> ~A, all_models=True)) {A: False} >>> use_models(satisfiable(A ^ A, all_models=True)) UNSAT dpll2z2Currently only dpll2 can handle using lra theory. z is not handled.pycosatzpycosat module is not present minisat22pysatz3dpllr)dpll_satisfiable)use_lra_theory)pycosat_satisfiable)minisat22_satisfiable)z3_satisfiable) rr ImportErrorsympy.logic.algorithms.dpllrsympy.logic.algorithms.dpll2&sympy.logic.algorithms.pycosat_wrapperr(sympy.logic.algorithms.minisat22_wrapperr!sympy.logic.algorithms.z3_wrapperrNotImplementedError) expr algorithm all_modelsminimalrrrrrrrrs r satisfiabler+#sT  Y'%9QR[Q\\lmn n I2 *  !II%!"ABB I+g& =I$ 4  :IF@%% g APP i N"444 k !R$Tw?? d Dd// rc4[[U55(+$)a@ 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-zs*3t9% %%rc^^^SSKJm SmUUU4SjmUT;aU$[U5nT"U5(d[SU-5eU(d0nUR 5VVs0sHup4UT;dM X4_M nnnUR U5nUT;a [ U5$U(aX[RUR5S5n[XQ5(a[U5(agg[U5(dggs snnf) 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)TFc>[UT5(dUT;ag[U[5(dg[U4SjUR55$)NTFc34># UH nT"U5v M g7fN).0arg _validates r -pl_true.._validate..s7Yc9S>>Ys) isinstancerallr)r'r/r6booleans rr6pl_true.._validates> dF # #tw$007TYY777rz$%s is not a valid boolean expressionTFN) sympy.core.symbolr/r ritemssubsbooldictfromkeysatomspl_truer-r+) r'modeldeepkvresultr/r6r;s @@@rrDrDsP)G8 w 4=D T???$FGG #kkm >> from sympy.abc import A, B, C >>> from sympy.logic.inference import entails >>> entails(A, [A >> B, B >> C]) False >>> entails(C, [A >> B, B >> C, A]) True >>> entails(A >> B) False >>> entails(A >> (B >> A)) True References ========== .. [1] https://en.wikipedia.org/wiki/Logical_consequence )listappendrr+r)r' formula_sets rentailsrNs;2;'  s4y!3 ,- --rcD\rSrSrSrS SjrSrSrSr\ S5r S r g) KBz"Base class for all knowledge basesNcT[5UlU(aURU5 ggr2)setclauses_tellselfsentences r__init__ KB.__init__s  IIh  rc[er2r&rVs rrUKB.tell!!rc[er2r\rWquerys raskKB.askr^rc[er2r\rVs rretract KB.retract r^rc>[[UR55$r2)rKrrT)rWs rclauses KB.clauses sGDMM*++r)rTr2) __name__ __module__ __qualname____firstlineno____doc__rYrUrbrepropertyrh__static_attributes__r3rrrPrPs-, """,,rrPc*\rSrSrSrSrSrSrSrg)PropKBiz=A KB for Propositional Logic. Inefficient, with no indexing.cp[[U55HnURRU5 M g)zAdd 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)rrrTaddrWrXcs rrU PropKB.tells**6(+,A MM  a -rc,[XR5$)zChecks 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 )rNrTr`s rrb PropKB.ask,s umm,,rcp[[U55HnURRU5 M g)zRemove 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)rrrTdiscardrus rrePropKB.retract>s**6(+,A MM ! !! $-rr3N) rjrkrlrmrnrUrbrerpr3rrrrrrsG!0-$%rrr)NFFF)NFr2)rnsympy.logic.boolalgrrrrrsympy.core.sortingrsympy.core.sympifyr sympy.external.importtoolsr rr+r-rDrNrPrrr3rrrsN&LL&&4@4Tn&0FR.B,,*C%RC%r