o o 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:|dus|dur |S|jr|S|jrt|jdStd)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)literalri/var/www/html/construction_image-detection-poc/venv/lib/python3.10/site-packages/sympy/logic/inference.pyr sr NFc Cs8|r|dur|dkrtd|dd}|dus|dkr1td}|dur'd}n |dkr/tdd}|dkr?td}|dur?d}|d krMtd }|durMd}|d kr[d d lm}||S|dkrld d lm}||||d S|dkr{d dlm} | ||S|dkrd dlm } | |||S|d krd dl m } | ||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 Ndpll2z2Currently 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_modelsminimalrrrrrrrrrrr satisfiable#sF*        r(cCstt| 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(rr$rrrvalidzsr*csddlmdfdd|vr|St|}|s$td||s(i}fdd|D}||}|vr@t|S|r]t| d }t ||rWt |rUd Sd St |s]d 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 |vr dSt|tsdStfdd|jDS)NTFc3s|]}|VqdSNr).0arg) _validaterr sz-pl_true.._validate..) isinstancerallr r)r+r/booleanrrr/s  zpl_true.._validatez$%s is not a valid boolean expressioncsi|] \}}|vr||qSrr)r-kv)r4rr szpl_true..TFN) sympy.core.symbolr+rritemssubsbooldictfromkeysatomspl_truer*r()r$modeldeepresultrr3rr?s. (   r?cCs.|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 )listappendrr(r)r$ formula_setrrrentailss  rFc@s>eZdZdZd ddZddZddZd d Zed d Z dS)KBz"Base class for all knowledge basesNcCst|_|r ||dSdSr,)setclauses_tellselfsentencerrr__init__sz KB.__init__cCtr,r#rKrrrrJzKB.tellcCrOr,rPrLqueryrrraskrQzKB.askcCrOr,rPrKrrrretract rQz KB.retractcCstt|jSr,)rCrrI)rLrrrclauses sz KB.clausesr,) __name__ __module__ __qualname____doc__rNrJrTrUpropertyrVrrrrrGs rGc@s(eZdZdZddZddZddZdS) PropKBz=A KB for Propositional Logic. Inefficient, with no indexing.cC"tt|D]}|j|qdS)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)rrrIaddrLrMcrrrrJz 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 )rFrIrRrrrrT,s z PropKB.askcCr])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)rrrIdiscardr_rrrrU>razPropKB.retractN)rWrXrYrZrJrTrUrrrrr\s  r\)NFFF)NFr,)rZsympy.logic.boolalgrrrrrsympy.core.sortingrsympy.core.sympifyrsympy.external.importtoolsr r r(r*r?rFrGr\rrrrs    W  I!