+ hHTRt^RIHt^RIHt^RIHtHt^RIH t H t ^RI H t H t HtHtHtHtHtHtHtHtHtHtHtHt!RR]4tRt!R R ]4t!R R ]4t!R R]4t !RR]4t!!RR4t"Rt#Rt$Rt%Rt&Rt'Rt(Rt)]*R8Xd ])!4R#R#)z A module to perform nonmonotonic reasoning. The ideas and demonstrations in this module are based on "Logical Foundations of Artificial Intelligence" by Michael R. Genesereth and Nils J. Nilsson. ) defaultdict)reduce)ProverProverCommandDecorator)Prover9Prover9Command)AbstractVariableExpression AllExpression AndExpressionApplicationExpressionBooleanExpressionEqualityExpressionExistsExpression Expression ImpExpressionNegatedExpressionVariableVariableExpressionoperatorunique_variablec]tRt^&tRtR#)ProverParseErrorN)__name__ __module__ __qualname____firstlineno____static_attributes__r=/usr/lib/python3/dist-packages/nltk/inference/nonmonotonic.pyrr&srrcxVfTpM W).,p\\PRV4\44#)Nc3@"TFqP4xK R#5iN) constants).0as& r get_domain../s H1s)rror_set)goal assumptionsall_expressionss&& r get_domainr-*s3 |%%/ (,, H H#% PPrc6a]tRt^2toRtRtRtRtRtVt R#)ClosedDomainProverzQ This is a prover decorator that adds domain closure assumptions before proving. cVPP4Uu.uFqNK ppVPP4p\W24pVUu.uFqPP WT4NK up#uupiuupir")_commandr+r*r-replace_quants)selfr%r+r*domainexs& rr+ClosedDomainProver.assumptions8sj"&--";";"=>"=Qq"= >}}!!#D.:EF+B##B/+FF?Gs A.A3cVPP4p\WPP44pVP W4#r")r1r*r-r+r2)r3r*r4s& rr*ClosedDomainProver.goal>s<}}!!#D--";";"=>""400rc  H\V\4'djVUu.uF1q1PPVP\ V44NK3 ppVUu.uFqPP WR4NK pp\RV4#\V\4'dGVPVP VPV4VP VPV44#\V\4'dVP VPV4)#\V\4'djVUu.uF1q1PPVP\ V44NK3 ppVUu.uFq0P W24NK pp\RV4#V#uupiuupiuupiuupi)a Apply the closed domain assumption to the expression - Domain = union([e.free()|e.constants() for e in all_expressions]) - translate "exists x.P" to "(z=d1 | z=d2 | ... ) & P.replace(x,z)" OR "P.replace(x, d1) | P.replace(x, d2) | ..." - translate "all x.P" to "P.replace(x, d1) & P.replace(x, d2) & ..." :param ex: ``Expression`` :param domain: set of {Variable}s :return: ``Expression`` cW,#r"rxys&&r3ClosedDomainProver.replace_quants..UqurcW,#r"rr;s&&rr>r?br@r) isinstancer termreplacevariablerr2rr __class__firstsecondrr)r3r5r4d conjunctsc disjunctss&&& rr2!ClosedDomainProver.replace_quantsCso b- ( (MSMS -?-BCV BKKA,,Q7IK,i8 8 - . .<<##BHHf5##BIIv6 - . .''88 8 , - -MSMS -?-BCV BKKA,,Q7IK,i8 8I'LLs7FF)7F&FrN) rrrr__doc__r+r*r2r__classdictcell__ __classdict__s@rr/r/2s G 1 !!rr/c*a]tRt^gtoRtRtRtVtR#)UniqueNamesProverzO This is a prover decorator that adds unique names assumptions before proving. c VPP4p\\VPP 4V44p\ 4pVF^p\ V\4'gKVPPpVPPpW5,PV4K` .p\V4FwrW(^,RFzp WV,9gK\\V4\V 44p \4PW4'dW4,PV 4KhVP!V )4K| K W,#)z - Domain = union([e.free()|e.constants() for e in all_expressions]) - if "d1 = d2" cannot be proven from the premises, then add "d1 != d2" N)r1r+listr-r* SetHolderrBr rGrErHadd enumeraterrproveappend) r3r+r4eq_setsr%avbvnew_assumptionsibnewEqExs & rr+UniqueNamesProver.assumptionsms mm//1 j!3!3!5{CD+A!/00WW%%XX&& # f%DAEG_AJ&0*1-/A!/DGyw<< q)(..x8%&,,rrN)rrrrrNr+rrOrPs@rrSrSgs "-"-rrSc*a]tRt^toRtRtRtVtR#)rVz A list of sets of Variables. c \V\4'gQhVF pW9gK Vu# V0pVPV4V#)z> :param item: ``Variable`` :return: the set containing 'item' )rBrrZ)r3itemsnews&& r __getitem__SetHolder.__getitem__sE $))))Ayf C rrN)rrrrrNrhrrOrPs@rrVrVs  rrVcBa]tRt^toRtRtRtRtRtRt Rt Vt R#) ClosedWorldProvera= This is a prover decorator that completes predicates before proving. If the assumptions contain "P(A)", then "all x.(P(x) -> (x=A))" is the completion of "P". If the assumptions contain "all x.(ostrich(x) -> bird(x))", then "all x.(bird(x) -> ostrich(x))" is the completion of "bird". If the assumptions don't contain anything that are "P", then "all x.-P(x)" is the completion of "P". walk(Socrates) Socrates != Bill + all x.(walk(x) -> (x=Socrates)) ---------------- -walk(Bill) see(Socrates, John) see(John, Mary) Socrates != John John != Mary + all x.all y.(see(x,y) -> ((x=Socrates & y=John) | (x=John & y=Mary))) ---------------- -see(Socrates, Mary) all x.(ostrich(x) -> bird(x)) bird(Tweety) -ostrich(Sam) Sam != Tweety + all x.(bird(x) -> (ostrich(x) | x=Tweety)) + all x.-ostrich(x) ------------------- -bird(Sam) c dVPP4pVPV4p.pVEFppW$,pVPV4pVUu.uFp\ V4NK pp.p VP FOp .p \ W4FwrV P\W44K! V P\RV 44KQ VPFKp/p\ W^,4F wrWV &K V PV^,PV44KM V 'd,VPWF4p\RV 4p\VV4pM\VPWF44pVRRR1,Fp\VV4pK VPV4EKs W,#uupi)cW,#r"rr;s&&rr>/ClosedWorldProver.assumptions..sQUrcW,#r"rr;s&&rr>rnsrN)r1r+_make_predicate_dict_make_unique_signaturer signaturesziprZr r propertiessubstitute_bindings_make_antecedentrrr )r3r+ predicatesr^p predHoldernew_sigv new_sig_exsrLsig equality_exsv1v2propbindings antecedent consequentaccum new_sig_vars& rr+ClosedWorldProver.assumptionssmm//1 ..{; A#J11*=G:AB'Q-a0'KBI",,! !+3FB ''(:2(BC4  (:L!IJ -#--!+Aw7FB#%RL8  a! #$6 B %j*=*$*?*?*KL 'tt}} %k59 -  " "5 )GJ,,ECsF-c \;QJd'.R\VP44FNK 5#!R\VP444#)z This method figures out how many arguments the predicate takes and returns a tuple containing that number of unique variables. c36"TFp\4xK R#5ir")r)r$r_s& rr&;ClosedWorldProver._make_unique_signature..sP0O1_&&0Os)tuplerange signature_len)r3rzs&&rrr(ClosedWorldProver._make_unique_signatures< uPj6N6N0OPuPuPj6N6N0OPPPrc >TpVFpV!\V44pK V#)zn Return an application expression with 'predicate' as the predicate and 'signature' as the list of arguments. )r)r3 predicate signaturerr|s&&& rrw"ClosedWorldProver._make_antecedents)  A#$6q$9:Jrc X\\4pVFpVPW24K V#)z Create a dictionary of predicates from the assumptions. :param assumptions: a list of ``Expression``s :return: dict mapping ``AbstractVariableExpression`` to ``PredHolder`` )r PredHolder_map_predicates)r3r+rxr%s&& rrq&ClosedWorldProver._make_predicate_dicts,!, A   /rc\V\4'dMVP4wr4\V\4'd#W#,P \ V44R#R#\V\ 4'd;VPVPV4VPVPV4R#\V\4'EdVP.pVPp\V\4'd*VPVP4VPpK?\V\4'Ed5\VP\4'Ed\VP\4'dVPP4wrxVPP4wr\V\4'd\V \4'dYXU u.uFqPNK up 8XdgYZU u.uFqPNK up 8XdFW),P\ V4VP34W',P!V4R#R#R#R#R#R#R#R#R#uup iuup ir")rBr uncurryr append_sigrr rrGrHr rErCrZr append_propvalidate_sig_len) r3 expressionpredDictfuncargsr~rCfunc1args1func2args2r|s &&& rr!ClosedWorldProver._map_predicatess j"7 8 8#++-JD$ :;;))%+6<  M 2 2  !1!18 <  !2!2H =  M 2 2&&'C??DT=11 4==)yy$ ..djj*?@@ZKK!6FF$(::#5#5#7LE#';;#6#6#8LE"5*DEE&u.HII#>1JJ#>>#>1JJ#>> 33U3Z4LM 88=??JF F@/3 $?#>s "I1I6rN) rrrrrNr+rrrwrqrrrOrPs@rrkrks*>+-ZQ >>rrkcHa]tRtRtoRtRtRtRtRtRt Rt R t Vt R #) ri/as This class will be used by a dictionary that will store information about predicates to be used by the ``ClosedWorldProver``. The 'signatures' property is a list of tuples defining signatures for which the predicate is true. For instance, 'see(john, mary)' would be result in the signature '(john,mary)' for 'see'. The second element of the pair is a list of pairs such that the first element of the pair is a tuple of variables and the second element is an expression of those variables that makes the predicate true. For instance, 'all x.all y.(see(x,y) -> know(x,y))' would result in "((x,y),('see(x,y)'))" for 'know'. c0.Vn.VnRVnR#r"rsrurr3s&r__init__PredHolder.__init__?s!rc^VPV4VPPV4R#r")rrsrZr3r{s&&rrPredHolder.append_sigDs" g& w'rclVPV^,4VPPV4R#)N)rrurZ)r3new_props&&rrPredHolder.append_propHs& hqk* x(rcVPf\V4VnR#VP\V48wd \R4hR#)NzSignature lengths do not match)rlen Exceptionrs&&rrPredHolder.validate_sig_lenLs=    %!$WD    3w< /<= =0rcVRVP RVP RVP R2#)(,)rrs&r__str__PredHolder.__str__Rs.4??#1T__$5Qt7I7I6J!LLrcRV,#)z%srrs&r__repr__PredHolder.__repr__Us d{r)rurrsN) rrrrrNrrrrrrrrOrPs@rrr/s. " ()> Mrrc\PpV!R4pV!R4pV!R4p\W1V.4p\VP 44\ V4p\R4VP 4Fp\RV4K \RVP44\VP 44V!R4pV!R4pV!R4pV!R4p\W1W'.4p\VP 44\ V4p\R4VP 4Fp\RV4K \RVP44\VP 44V!R4pV!R4pV!R4pV!R4p\W1W'.4p\VP 44\ V4p\R4VP 4Fp\RV4K \RVP44\VP 44V!R4pV!R4pV!R4p\W1V.4p\VP 44\ V4p\R4VP 4Fp\RV4K \RVP44\VP 44V!R 4pV!R 4pV!R 4pV!R 4pV!R 4p V!R4p\W1W'W.4p\VP 44\ V4p\R4VP 4Fp\RV4K \RVP44\VP 44R#)zexists x.walk(x) man(Socrates)walk(Socrates) assumptions: goal: -walk(Bill)z walk(Bill)z all x.walk(x)z girl(mary)z dog(rover)zall x.(girl(x) -> -dog(x))zall x.(dog(x) -> -girl(x))zchase(mary, rover)z1exists y.(dog(y) & all x.(girl(x) -> chase(x,y)))N)r fromstringrprintrYr/r+r*) lexprp1p2rKprovercdpr%p3p4p5s rclosed_domain_demorYs  ! !E " #B  B  A ABx (F &,,. V $C . __  eQ '388: #))+ " #B  B ~ B  A AB| ,F &,,. V $C . __  eQ '388: #))+ " #B  B ~ B  A AB| ,F &,,. V $C . __  eQ '388: #))+  !B } B A ABx (F &,,. V $C . __  eQ '388: #))+ } B } B , -B , -B $ %B BCA ABB3 4F &,,. V $C . __  eQ '388: #))+rc\PpV!R4pV!R4pV!R4p\W1V.4p\VP 44\ V4p\R4VP 4Fp\RV4K \RVP44\VP 44V!R4pV!R4pV!R4pV!R 4p\W1W'.4p\VP 44\ V4p\R4VP 4Fp\RV4K \RVP44\VP 44R #) rz man(Bill)zexists x.exists y.(x != y)rrrz!all x.(walk(x) -> (x = Socrates))zBill = Williamz Bill = Billyz-walk(William)N)rrrrrYrSr+r*)rrrrKrunpr%rs runique_names_demors$  ! !E  B | B +,A ABx (F &,,. F #C . __  eQ '388: #))+ 3 4B  !B  B  A AB| ,F &,,. F #C . __  eQ '388: #))+rcf\PpV!R4pV!R4pV!R4p\W1V.4p\VP 44\ V4p\R4VP 4Fp\RV4K \RVP44\VP 44V!R4pV!R4pV!R4pV!R 4pV!R 4p\W1W'V.4p\VP 44\ V4p\R4VP 4Fp\RV4K \RVP44\VP 44V!R 4pV!R 4pV!R 4pV!R4pV!R4p\W1W'V.4p\VP 44\ V4p\R4VP 4Fp\RV4K \RVP44\VP 44R#)rz(Socrates != Bill)rrrrsee(Socrates, John)see(John, Mary)z(Socrates != John)z(John != Mary)-see(Socrates, Mary)zall x.(ostrich(x) -> bird(x))z bird(Tweety)z -ostrich(Sam)z Sam != Tweetyz -bird(Sam)N)rrrrrYrkr+r*) rrrrKrcwpr%rrs rclosed_world_demors  ! !E  !B $ %B nA ABx (F &,,. F #C . __  eQ '388: #))+ % &B ! "B $ %B  !B %&A ABB/ 0F &,,. F #C . __  eQ '388: #))+ / 0B  B  B  B mA ABB/ 0F &,,. F #C . __  eQ '388: #))+rcR\PpV!R4pV!R4pV!R4p\W1V.4p\VP 44\ \ \V444pVP4Fp\V4K \VP 44R#)rrrN) rrrrrYr/rSrkr+)rrrrKrcommandr%s rcombination_prover_demors  ! !E % &B ! "B %&A ABx (F &,,. !23DV3L!MNG  " a# '--/rcz\Pp.pVPV!R44VPV!R44VPV!R44VPV!R44VPV!R44VPV!R44VPV!R44VPV!R44VPV!R44VPV!R 44VPV!R 44VPV!R 44VPV!R 44VPV!R 44\RV4p\ \ V44pVP 4Fp\V4K \RV4\RV4\RV4R#)z'all x.(elephant(x) -> animal(x))z'all x.(bird(x) -> animal(x))z%all x.(dove(x) -> bird(x))z%all x.(ostrich(x) -> bird(x))z(all x.(flying_ostrich(x) -> ostrich(x))z)all x.((animal(x) & -Ab1(x)) -> -fly(x))z(all x.((bird(x) & -Ab2(x)) -> fly(x))z)all x.((ostrich(x) & -Ab3(x)) -> -fly(x))z#all x.(bird(x) -> Ab1(x))z#all x.(ostrich(x) -> Ab2(x))z#all x.(flying_ostrich(x) -> Ab3(x))z elephant(E)zdove(D)z ostrich(O)Nz-fly(E)zfly(D)z-fly(O)) rrrZrrSrkr+r print_proof)rpremisesrrr%s rdefault_reasoning_demorsx  ! !EH OOEDEF OOEDEF OOEBCD OOEBCD OOEEFG OO :; OO 9: OO :;  OOE@AB OOE@AB OOE@AB OOE.)* OOE*%& OOE-()D( +F 1& 9:G  " a# 8$(# 8$rc\Pp\V!V4V4p\\ V44p\ WP 4VP 44R#r")rrrrSrkrrY)r*rrrrs&& rrr!sC  ! !E E$K 2F 1& 9:G $  0rcj\4\4\4\4\ 4R#r")rrrrrrrrdemor(s r__main__N)+rN collectionsr functoolsrnltk.inference.apirrnltk.inference.prover9rrnltk.sem.logicrr r r r r rrrrrrrrrrr-r/rSrUrVrkrrrrrrrrrrrrrs $=:$ y Q2/2j(-.(-V(F>.F>R''TBJ:)X )%X1 zFr