QdJ|dZddlmZddlmZddlmZmZddlm Z m Z ddl m Z m Z mZmZmZmZmZmZmZmZmZmZmZmZGddeZd ZGd d eZGd d eZGddeZ GddeZ!GddZ"dZ#dZ$dZ%dZ&dZ'dZ(dZ)e*dkr e)dSdS)z A module to perform nonmonotonic reasoning. The ideas and demonstrations in this module are based on "Logical Foundations of Artificial Intelligence" by Michael R. Genesereth and Nils J. Nilsson. ) defaultdict)reduce)ProverProverCommandDecorator)Prover9Prover9Command)AbstractVariableExpression AllExpression AndExpressionApplicationExpressionBooleanExpressionEqualityExpressionExistsExpression Expression ImpExpressionNegatedExpressionVariableVariableExpressionoperatorunique_variableceZdZdS)ProverParseErrorN)__name__ __module__ __qualname__;lib/python3.11/site-packages/nltk/inference/nonmonotonic.pyrr&sDrrc|||}n|| gz}ttjd|DtS)Nc3>K|]}|VdSN) constants.0as r zget_domain../s* H H1 H H H H H Hr)rror_set)goal assumptionsall_expressionss r get_domainr,*sC |%%$/ (, H H H H H#%% P PPrc$eZdZdZdZdZdZdS)ClosedDomainProverz] This is a prover decorator that adds domain closure assumptions before proving. cdjD}j}t||fd|DS)Ncg|]}|Srrr#s r z2ClosedDomainProver.assumptions..9s>>>Qq>>>rc<g|]}|Srreplace_quants)r$exdomainselfs rr1z2ClosedDomainProver.assumptions..<s)FFFB##B//FFFr)_commandr*r)r,)r7r*r)r6s` @rr*zClosedDomainProver.assumptions8sd>>$-";";"="=>>> }!!##D+..FFFFF+FFFFrc|j}t||j}|||Sr!)r8r)r,r*r4)r7r)r6s rr)zClosedDomainProver.goal>sH}!!##D$-";";"="=>>""4000rc4ttr.fdD}fd|D}td|SttrHjjSttrj  Sttr.fdD}fd|D}td|SS)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`` cjg|]/}jjt|0Srtermreplacevariablerr$dr5s rr1z5ClosedDomainProver.replace_quants..QAHI -?-B-BCCrc<g|]}|Srr3)r$cr6r7s rr1z5ClosedDomainProver.replace_quants..T)KKKA,,Q77KKKrc ||zSr!rxys rz3ClosedDomainProver.replace_quants..U q1urcjg|]/}jjt|0Srr<r@s rr1z5ClosedDomainProver.replace_quants..^rBrc<g|]}|Srr3)r$rAr6r7s rr1z5ClosedDomainProver.replace_quants..arErc ||zSr!rrGs rrJz3ClosedDomainProver.replace_quants..brKr) isinstancer rr __class__r4firstsecondrr=r)r7r5r6 conjuncts disjunctss``` rr4z!ClosedDomainProver.replace_quantsCsj b- ( ( MSILKKKKKKKI,,i88 8 - . . <<##BHf55##BIv66 - . . ''888 8 , - - MSILKKKKKKKI,,i88 8IrN)rrr__doc__r*r)r4rrrr.r.2sN GGG 111 !!!!!rr.ceZdZdZdZdS)UniqueNamesProverz[ This is a prover decorator that adds unique names assumptions before proving. c|j}tt|j|}t }|D]J}t |tr3|jj }|j j }|| |Kg}t|D]\}}||dzdD]} | ||vr~tt|t| } t| |r|| | t|| ||zS)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)r8r*listr,r) SetHolderrOrrQr?rRadd enumeraterrproveappend) r7r*r6eq_setsr%avbvnew_assumptionsibnewEqExs rr*zUniqueNamesProver.assumptionsmse m//11 j!3!3!5!5{CCDD++ $ $A!/00 $W%X& ###f%% 9 9DAqAEGG_ 9 9GAJ&&0*1--/A!/D/DGyyw <<9  q))))(..x888 9_,,rN)rrrrUr*rrrrWrWgs- "-"-"-"-"-rrWceZdZdZdZdS)r[z& A list of sets of Variables. c~t|tsJ|D] }||vr|cS |h}|||S)zV :param item: ``Variable`` :return: the set containing 'item' )rOrr_)r7itemsnews r __getitem__zSetHolder.__getitem__s` $)))))  Aqyyf C rN)rrrrUrlrrrr[r[s-     rr[c0eZdZdZdZdZdZdZdZdS)ClosedWorldProvera This is a prover decorator that completes predicates before proving. If the assumptions contain "P(A)", then "all x.(P(x) -> (x=A))" is the completion of "P". If the assumptions contain "all x.(ostrich(x) -> bird(x))", then "all x.(bird(x) -> ostrich(x))" is the completion of "bird". If the assumptions don't contain anything that are "P", then "all x.-P(x)" is the completion of "P". walk(Socrates) Socrates != Bill + all x.(walk(x) -> (x=Socrates)) ---------------- -walk(Bill) see(Socrates, John) see(John, Mary) Socrates != John John != Mary + all x.all y.(see(x,y) -> ((x=Socrates & y=John) | (x=John & y=Mary))) ---------------- -see(Socrates, Mary) all x.(ostrich(x) -> bird(x)) bird(Tweety) -ostrich(Sam) Sam != Tweety + all x.(bird(x) -> (ostrich(x) | x=Tweety)) + all x.-ostrich(x) ------------------- -bird(Sam) c x|j}||}g}|D]}||}||}d|D}g}|jD]a} g} t || D](\} } | t| | )|td| b|j D]S} i}t || dD] \} } | || < || d |T|r8| ||}td|}t||}n#t| ||}|dddD]}t||}||||zS)Nc,g|]}t|Srrr$vs rr1z1ClosedWorldProver.assumptions..s!BBBQ-a00BBBrc ||zSr!rrGs rrJz/ClosedWorldProver.assumptions..s QUrrrYc ||zSr!rrGs rrJz/ClosedWorldProver.assumptions..s Qr)r8r*_make_predicate_dict_make_unique_signature signatureszipr_rr propertiessubstitute_bindings_make_antecedentrrr )r7r* predicatesrcp predHoldernew_sig new_sig_exsrTsig equality_exsv1v2propbindings antecedent consequentaccum new_sig_vars rr*zClosedWorldProver.assumptionssm//11 ..{;; # *# *A#AJ11*==GBB'BBBKI", K K! !+s33DDFB ''(:2r(B(BCCCC  (:(:L!I!IJJJJ#- H H!+tAw77&&FB#%HRLL  a!> #$6$6 BB %j*==*$*?*?7*K*KLL 'ttt} : : %k599  " "5 ) ) ) )_,,rcXtdt|jDS)z This method figures out how many arguments the predicate takes and returns a tuple containing that number of unique variables. c32K|]}tVdSr!)r)r$rds rr&z;ClosedWorldProver._make_unique_signature..s(PP1_&&PPPPPPr)tuplerange signature_len)r7rs rrxz(ClosedWorldProver._make_unique_signatures, PPj6N0O0OPPPPPPrcD|}|D]}|t|}|S)z Return an application expression with 'predicate' as the predicate and 'signature' as the list of arguments. rq)r7 predicate signaturerrss rr}z"ClosedWorldProver._make_antecedents8   ; ;A#$6q$9$9::JJrcdtt}|D]}||||S)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)r7r*r~r%s rrwz&ClosedWorldProver._make_predicate_dicts?!,,  0 0A  J / / / /rct|trX|\}}t|tr*||t |dSdSt|t r8||j|||j |dSt|trr|j g}|j }t|tr6| |j |j }t|t6t|trt|jtrt|j tr|j\}}|j \} } t|trt| trv|d|Dkrh|d| DkrZ|| t ||jf|||dSdSdSdSdSdSdSdSdS)Ncg|] }|j Srr?rrs rr1z5ClosedWorldProver._map_predicates..(#>#>#>1AJ#>#>#>rcg|] }|j Srrrrs rr1z5ClosedWorldProver._map_predicates..)rr)rOr uncurryr append_sigrr rrQrRr r?r=r_r append_propvalidate_sig_len) r7 expressionpredDictfuncargsrr=func1args1func2args2s rrz!ClosedWorldProver._map_predicatessw j"7 8 8 >#++--JD$$ :;; 7))%++66666 7 7  M 2 2 >  !18 < < <  !2H = = = = =  M 2 2 >&'C?DT=11 ! 4=)))yT=11 !$ .. >dj*?@@ >ZK!6FF >$(:#5#5#7#7LE5#';#6#6#8#8LE5"5*DEE>&u.HII> #>#>#>#>#>>>#>#>#>#>#>>> 33U3ZZ4LMMM 88=====) > > > > > > > > >>>>?>>>rN) rrrrUr*rxr}rwrrrrrnrnsm>+-+-+-ZQQQ   >>>>>rrnc6eZdZdZdZdZdZdZdZdZ dS) ra 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'. c0g|_g|_d|_dSr!ryr{rr7s r__init__zPredHolder.__init__?s!rcd|||j|dSr!)rryr_r7rs rrzPredHolder.append_sigDs2 g&&& w'''''rcp||d|j|dS)Nr)rr{r_)r7new_props rrzPredHolder.append_propHs6 hqk*** x(((((rc|jt||_dS|jt|krtddS)NzSignature lengths do not match)rlen Exceptionrs rrzPredHolder.validate_sig_lenLsJ   %!$WD     3w<< / /<== =0 /rc8d|jd|jd|jdS)N(,)rrs r__str__zPredHolder.__str__Rs*L4?LLT_LLt7ILLLLrc d|zS)Nz%srrs r__repr__zPredHolder.__repr__Us d{rN) rrrrUrrrrrrrrrrr/s{  """ ((()))>>> MMMrrc. tj}|d}|d}|d}t|||g}t|t |}td|D]}td|td|t||d}|d}|d}|d}t||||g}t|t |}td|D]}td|td|t||d}|d}|d}|d}t||||g}t|t |}td|D]}td|td|t||d}|d}|d }t|||g}t|t |}td|D]}td|td|t||d }|d }|d }|d }|d} |d}t|||||| g}t|t |}td|D]}td|td|t|dS)Nzexists 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))))r fromstringrprintr^r.r*r)) lexprp1p2rDprovercdpr%p3p4p5s rclosed_domain_demorYsX  !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 BCCA ABB3 4 4F &,,.. V $ $C . __   eQ '388:: #))++rctj}|d}|d}|d}t|||g}t|t |}td|D]}td|td|t||d}|d}|d }|d }t||||g}t|t |}td|D]}td|td|t|dS) Nrz man(Bill)zexists x.exists y.(x != y)rrrz!all x.(walk(x) -> (x = Socrates))zBill = Williamz Bill = Billyz-walk(William))rrrrr^rWr*r))rrrrDrunpr%rs runique_names_demors  !E  B |  B +,,A ABx ( (F &,,.. F # #C . __   eQ '388:: #))++ 3 4 4B  ! !B   B   A AB| , ,F &,,.. F # #C . __   eQ '388:: #))++rctj}|d}|d}|d}t|||g}t|t |}td|D]}td|td|t||d}|d}|d }|d }|d }t|||||g}t|t |}td|D]}td|td|t||d }|d }|d}|d}|d}t|||||g}t|t |}td|D]}td|td|t|dS)Nrz(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))rrrrr^rnr*r)) rrrrDrcwpr%rrs rclosed_world_demors  !E  ! !B $ % %B nA ABx ( (F &,,.. F # #C . __   eQ '388:: #))++ % & &B ! " "B $ % %B  ! !B %&&A ABB/ 0 0F &,,.. F # #C . __   eQ '388:: #))++ / 0 0B   B  B  B mA ABB/ 0 0F &,,.. F # #C . __   eQ '388:: #))++rctj}|d}|d}|d}t|||g}t|t t t|}|D]}t|t|dS)Nrrr) rrrrr^r.rWrnr*)rrrrDrcommandr%s rcombination_prover_demors  !E % & &B ! " "B %&&A ABx ( (F &,,.. !23DV3L3L!M!MNNG  " " a '--//rcntj}g}||d||d||d||d||d||d||d||d||d ||d ||d ||d ||d ||dtd|}t t |}|D]}t|td|td|td|dS)Nz'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)z-fly(E)zfly(D)z-fly(O)) rrr_rrWrnr*r print_proof)rpremisesrrr%s rdefault_reasoning_demorsH  !EH OOEEDEEFFF OOEEDEEFFF OOEEBCCDDD OOEEBCCDDD OOEEEFFGGG OO :;; OO 9:: OO :;;  OOEE@AABBB OOEE@AABBB OOEE@AABBB OOEE.))*** OOEE*%%&&& OOEE-(()))D( + +F 1& 9 9::G  " " a 8$$$(### 8$$$$$rctj}t|||}tt |}t |||dSr!)rrrrWrnrr^)r)rrrrs rrr!s_  !E EE$KK 2 2F 1& 9 9::G $  00000rcttttt dSr!)rrrrrrrrdemor(sDr__main__N)+rU collectionsr functoolsrnltk.inference.apirrnltk.inference.prover9rrnltk.sem.logicr r r r r rrrrrrrrrrrr,r.rWrZr[rnrrrrrrrrrrrrrs $#####========::::::::$     y   QQQ22222/222j(-(-(-(-(-.(-(-(-V(F>F>F>F>F>.F>F>F>R''''''''TBBBJ:)))X   )%)%)%X111 zDFFFFFr