+ i#Rt^RIHtHtHtHtHt^RIHt^RI H t ^RI H t Rt RRltRtRR ltRR lt!R R 4t!R R]4tR#)z Inference in propositional logic)AndNot conjunctsto_cnfBooleanFunction)ordered)sympify) import_modulecVRJgVRJdV#VP'dV#VP'd\VP^,4#\ R4h)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 TFz#Argument must be a boolean literal.) is_Symbolis_Notliteral_symbolargs ValueError)literals&u/Users/tonyclaw/.openclaw/workspace/skills/math-calculator/venv/lib/python3.14/site-packages/sympy/logic/inference.pyr r sP $'U*     gll1o..>??NcV'dVeVR8wd\RV R24hRpVeVR8Xd'\R4pVeRpMVR8Xd \R4hRpVR8Xd\R4pVfRpVR8Xd\R4pVfRpVR 8Xd^R IHpV!V4#VR8Xd^R IHpV!WVR 7#VR8Xd^R IHp V !W4#VR8Xd^R IH p V !WV4#VR8Xd^RI H p V !W4#\h)aJ Check satisfiability of a propositional sentence. Returns a model when it succeeds. Returns {true: true} for trivially true expressions. On setting all_models to True, if given expr is satisfiable then returns a generator of models. However, if expr is unsatisfiable then returns a generator containing the single element False. Examples ======== >>> from sympy.abc import A, B >>> from sympy.logic.inference import satisfiable >>> satisfiable(A & ~B) {A: True, B: False} >>> satisfiable(A & ~A) False >>> satisfiable(True) {True: True} >>> next(satisfiable(A & ~A, all_models=True)) False >>> models = satisfiable((A >> B) & B, all_models=True) >>> next(models) {A: False, B: True} >>> next(models) {A: True, B: True} >>> def use_models(models): ... for model in models: ... if model: ... # Do something with the model. ... print(model) ... else: ... # Given expr is unsatisfiable. ... print("UNSAT") >>> use_models(satisfiable(A >> ~A, all_models=True)) {A: False} >>> use_models(satisfiable(A ^ A, all_models=True)) UNSAT dpll2z2Currently only dpll2 can handle using lra theory. z is not handled.pycosatzpycosat module is not present minisat22pysatz3dpll)dpll_satisfiable)use_lra_theory)pycosat_satisfiable)minisat22_satisfiable)z3_satisfiable) rr ImportErrorsympy.logic.algorithms.dpllrsympy.logic.algorithms.dpll2&sympy.logic.algorithms.pycosat_wrapperr(sympy.logic.algorithms.minisat22_wrapperr!sympy.logic.algorithms.z3_wrapperrNotImplementedError) expr algorithm all_modelsminimalrrrrrrrrs &&&&& r satisfiabler*#sT  Y'%9QR[Q\\lmn n I2 *  !II%!"ABB I+g& =I$ 4  :IF@%% g APP i N"444 k !R$Tw?? d Dd// rc4\\V44'*#)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% %%rcaaa^RIHoRoVVV3RloVS9dV#\V4pS!V4'g\RV,4hV'g/pVP 4UUu/uFwr4VS9gKW4bK pppVP V4pVS9d \ V4#V'd_\PVP4R4p\WQ4'd\V4'dR#R#\V4'gR#R#uuppi)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 )SymbolTFc<\VS4'gVS9dR#\V\4'gR#\;QJd)V3RlVP4F 'dK R# R#!V3RlVP44#)TFc34<"TF pS!V4xK R#5iN).0arg _validates& r -pl_true.._validate..s7Yc9S>>Ys) isinstancerallr)r&r.r5booleans&rr5pl_true.._validatesZ dF # #tw$00s7TYY7ss7s7s7TYY777rz$%s is not a valid boolean expressionN)TF) sympy.core.symbolr.rritemssubsbooldictfromkeysatomspl_truer,r*) r&modeldeepkvresultr.r5r:s &&& @@@rrCrCsP)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&&rentailsrMs;2;'  s4y!3 ,- --rcPa]tRt^toRtR RltRtRtRt] R4t Rt Vt R#) KBz"Base class for all knowledge basesNcZ\4VnV'dVPV4R#R#r1)setclauses_tellselfsentences&&r__init__ KB.__init__s  IIh  rc\hr1r%rTs&&rrSKB.tell!!rc\hr1rZrUquerys&&raskKB.askr\rc\hr1rZrTs&&rretract KB.retract r\rc>\\VP44#r1)rJrrR)rUs&rclauses KB.clauses sGDMM*++r)rRr1) __name__ __module__ __qualname____firstlineno____doc__rWrSr`rcpropertyrf__static_attributes____classdictcell__ __classdict__s@rrOrOs0, """,,rrOc6a]tRtRtoRtRtRtRtRtVt R#)PropKBiz=A KB for Propositional Logic. Inefficient, with no indexing.c r\\V44FpVPPV4K R#)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)rrrRaddrUrVcs&& rrS PropKB.tells**6(+,A MM  a -rc ,\WP4#)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 )rMrRr^s&&rr` PropKB.ask,s umm,,rc r\\V44FpVPPV4K R#)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)rrrRdiscardrvs&& rrcPropKB.retract>s**6(+,A MM ! !! $-rr2N) rhrirjrkrlrSr`rcrnrorps@rrsrssG!0-$%%rrs)NFFF)NFr1)rlsympy.logic.boolalgrrrrrsympy.core.sortingrsympy.core.sympifyrsympy.external.importtoolsr r r*r,rCrMrOrsr2rrrsN&LL&&4@4Tn&0FR.B,,*C%RC%r