³ò ŽB_Kc@sŠddklZddkTddklZddklZlZdefd„ƒYZ defd„ƒYZ d efd „ƒYZ d e fd „ƒYZ d „Zd„Zd#d#d„Zd„Zd„Zd„Zd„Zdefd„ƒYZd#d„Zd„Zdefd„ƒYZdefd„ƒYZdefd„ƒYZd„Zd„Zd „Zd!„Z e!d"jo e ƒnd#S($iÿÿÿÿ(t defaultdict(t*(t skolemize(tProvertBaseProverCommandtProverParseErrorcBseZRS((t__name__t __module__(((s//p/zhu/06/nlp/nltk/nltk/inference/resolution.pyRstResolutionProvercBs/eZdZeZeeed„Zd„ZRS(tANSWERcCsú|p g}nt}y{g}|o|it| ƒƒnx!|D]}|it|ƒƒqFW|i|ƒ\}}|oti|ƒGHnWn[tj oO}|io&t|ƒi dƒot }g}qð|o |GHqð|‚nX||fS(sð @param goal: Input expression to prove @type goal: L{logic.Expression} @param assumptions: Input expressions to use as assumptions in the proof @type assumptions: L{list} of logic.Expression objects s maximum recursion depth exceeded( tNonetextendtclausifyt_attempt_prooftResolutionProverCommandt_decorate_clausest RuntimeErrort _assume_falsetstrt startswithtFalse(tselftgoalt assumptionstverbosetresulttclausestate((s//p/zhu/06/nlp/nltk/nltk/inference/resolution.pyt_proves*     cCsZttƒ}d}x;|t|ƒjo'||iƒp||o||dd}n |d}xÚ|t|ƒjoÂ||jo§|o ||iƒ oŽ||i|ƒ||i||ƒ}|o[xM|D]E}|d|df|_|i|ƒt|ƒpt|fSqÖqÖWd}Pq.n|d7}qgWn|d7}qWt|fS(Niiÿÿÿÿi( Rtlisttlent is_tautologytappendtunifyt_parentstTrueR(RRttriedtitjt newclausest newclause((s//p/zhu/06/nlp/nltk/nltk/inference/resolution.pyR 7s.   &   ( RRt ANSWER_KEYR$RR RRR (((s//p/zhu/06/nlp/nltk/nltk/inference/resolution.pyRsRcBsAeZeeed„Zed„Zed„Zed„ƒZRS(cCsT|dj ot|tƒpt‚n tƒ}ti||||ƒd|_dS(sø @param goal: Input expression to prove @type goal: L{logic.Expression} @param assumptions: Input expressions to use as assumptions in the proof. @type assumptions: C{list} of L{logic.Expression} N(R t isinstanceRtAssertionErrorRt__init__t_clauses(RRRtprover((s//p/zhu/06/nlp/nltk/nltk/inference/resolution.pyR-Xs   cCsc|itjoL|ii|iƒ|iƒ|ƒ\|_}||_ti|ƒ|_ n|iS(sh Perform the actual proof. Store the result to prevent unnecessary re-proving. ( t_resultR t_proverRRRR.RRt_proof(RRR((s//p/zhu/06/nlp/nltk/nltk/inference/resolution.pytprovehs  cCsœ|i|ƒtƒ}tttiƒƒ}xj|iD]_}xV|D]N}t|tƒo8|i |jo(t|i t ƒ o|i |i ƒqBqBWq5W|S(N( R3tsettVariableExpressiontVariableRR*R.R+tApplicationExpressiontfunctiontargumenttIndividualVariableExpressiontadd(RRtanswerst answer_extclausetterm((s//p/zhu/06/nlp/nltk/nltk/inference/resolution.pyt find_answersus   c Cs.d}tg}|D]}|tt|ƒƒq~ƒ}ttt|ƒƒƒ}xÖtt|ƒƒD]Â}d}d}||iƒo d}n||iot||iƒ}nd|tt||ƒƒd|}d|tt|dƒƒt|dƒ} |d| ||||f7}qdW|S(s, Decorate the proof output. ttAt Tautologyt is[%s] %s %s %s (tmaxRRtrangeR R#( Rtoutt_[1]R>tmax_clause_lent max_seq_lenR&tparentsttauttseq((s//p/zhu/06/nlp/nltk/nltk/inference/resolution.pyR‚s3 &,"( RRR R-RR3R@t staticmethodR(((s//p/zhu/06/nlp/nltk/nltk/inference/resolution.pyRWs tClausecBs‰eZd„Zeeeed„Zd„Zd„Zd„Zd„Z d„Z d„Z d„Z d „Z d „Zd „Zd „ZRS( cCs&ti||ƒd|_d|_dS(N(RR-R t _is_tautologyR#(Rtdata((s//p/zhu/06/nlp/nltk/nltk/inference/resolution.pyR-—s c Csg|tjo tƒ}n|tjoggf}n|tjoggf}nt|tƒot|ƒ}nt|||||t|ƒ}g}xƒt|ƒD]u\}} ||jo\xYt|ƒD]G\} } || jo.| |jo!| i| ƒo|i | ƒqËqËWq¥q¥Wg} x<t t |ƒƒD](}||jo| i ||ƒq7q7W| S(sÝ Attempt to unify this Clause with the other, returning a list of resulting, unified, Clauses. @param other: C{Clause} with which to unify @param bindings: C{BindingDict} containing bindings that should be used during the unification @param used: C{tuple} of two C{list}s of atoms. The first lists the atoms from 'self' that were successfully unified with atoms from 'other'. The second lists the atoms from 'other' that were successfully unified with atoms from 'self'. @param skipped: C{tuple} of two C{Clause}s. The first is a list of all the atoms from the 'self' Clause that have not been unified with anything on the path. The second is same thing for the 'other' Clause. @param debug: C{bool} indicating whether debug statements should print @return: C{list} containing all the resulting C{Clause}s that could be obtained by unification ( R t BindingDictR+tboolt DebugObjectt_iterate_firstt_complete_unify_patht enumeratetsubsumesR!RFR( RtothertbindingstusedtskippedtdebugR(tsubsumedR&tc1R'tc2R((s//p/zhu/06/nlp/nltk/nltk/inference/resolution.pyR"œs&    * cCs*x#|D]}||jotSqqWtS(sŽ Return True iff every term in 'self' is a term in 'other'. @param other: C{Clause} @return: C{bool} (RR$(RRYR((s//p/zhu/06/nlp/nltk/nltk/inference/resolution.pyt isSubsetOfÅs   c Csªg}x@|D]8}t|tƒo|i|iƒq |i| ƒq Wt|ƒ}tƒ}ggf}ggf}ttƒ}tt |||||t |ƒƒdjS(s÷ Return True iff 'self' subsumes 'other', this is, if there is a substitution such that every term in 'self' can be unified with a term in 'other'. @param other: C{Clause} @return: C{bool} i( R+tNegatedExpressionR!R?RORRRTRRRUt_subsumes_finalize( RRYt negatedothertatomtnegatedotherClauseRZR[R\R]((s//p/zhu/06/nlp/nltk/nltk/inference/resolution.pyRXÑs      cCstti|||ƒƒS(N(RORt __getslice__(Rtstarttend((s//p/zhu/06/nlp/nltk/nltk/inference/resolution.pyRgìscCs6tg}|D]}||jo ||qq~ƒS(N(RO(RRYRHR((s//p/zhu/06/nlp/nltk/nltk/inference/resolution.pyt__sub__ïscCstti||ƒƒS(N(RORt__add__(RRY((s//p/zhu/06/nlp/nltk/nltk/inference/resolution.pyRkòscCsü|itj o |iSnxÑt|ƒD]Ã\}}t|tƒp§t|ƒd}x”||jo‚||}t|tƒo%|i|jot|_tSqØn6t|tƒo%||ijot|_tSqØn|d8}qWWq(q(Wt |_t S(s Self is a tautology if it contains ground terms P and -P. The ground term, P, must be an exact match, ie, not using unification. i( RPR RWR+tEqualityExpressionRRbR?R$R(RR&RR'tb((s//p/zhu/06/nlp/nltk/nltk/inference/resolution.pyR õs&        cCs1tƒ}x!|D]}||itƒO}qW|S(N(R4tfreeR(RtsRe((s//p/zhu/06/nlp/nltk/nltk/inference/resolution.pyRn s  cCs1tg}|D]}||i||ƒq~ƒS(sà Replace every instance of variable with expression across every atom in the clause @param variable: C{Variable} @param expression: C{Expression} (ROtreplace(Rtvariablet expressionRHRe((s//p/zhu/06/nlp/nltk/nltk/inference/resolution.pyRpscCs.tg}|D]}||i|ƒq~ƒS(sÉ Replace every binding @param bindings: A C{list} of tuples mapping Variable Expressions to the Expressions to which they are bound @return: C{Clause} (ROtsubstitute_bindings(RRZRHRe((s//p/zhu/06/nlp/nltk/nltk/inference/resolution.pyRsscCs6ddig}|D]}|t|ƒq~ƒdS(Nt{s, t}(tjoinR(RRHtitem((s//p/zhu/06/nlp/nltk/nltk/inference/resolution.pyt__str__'scCs t|ƒS(N(R(R((s//p/zhu/06/nlp/nltk/nltk/inference/resolution.pyt__repr__*s(RRR-R RR"RaRXRgRjRkR RnRpRsRxRy(((s//p/zhu/06/nlp/nltk/nltk/inference/resolution.pyRO–s )       cCsf|id|||fƒt|ƒ pt|ƒ o|||||||ƒSnt|||||||dƒ}|d|dg|df}|t|d||||||dƒ7}yŠt|d|d||ƒ\} } } |d|d| d} |d|d| d} |t| | | | ggf||dƒ7}Wntj onX|SdS(sF This method facilitates movement through the terms of 'self' sunify(%s,%s) %siiN(tlineRt_iterate_secondRUt _unify_termstBindingException(tfirsttsecondRZR[R\tfinalize_methodR]Rt newskippedt newbindingstnewusedtunusedtnewfirstt newsecond((s//p/zhu/06/nlp/nltk/nltk/inference/resolution.pyRU-s"*&0cCs@|id|||fƒt|ƒ pt|ƒ o|||||||ƒSnê|d|d|dgf}t||d|||||dƒ}yŠt|d|d||ƒ\} } } |d|d| d} |d|d| d} |t| | | | ggf||dƒ7}Wntj onX|SdS(sG This method facilitates movement through the terms of 'other' sunify(%s,%s) %siiN(RzRR{R|R}(R~RRZR[R\R€R]RRR‚RƒR„R…R†((s//p/zhu/06/nlp/nltk/nltk/inference/resolution.pyR{Js&&0cCs t|tƒpt‚t|tƒpt‚|tjo tƒ}n|tjoggf}nt|tƒoWt|tƒoGt|i||ƒ}|d|g|d|gf}ggf}n2t|tƒoWt|tƒoGt||i|ƒ}|d|g|d|gf}ggf}nËt|t ƒoLt|i i |i fgƒ}|d|g|df}g|gf}not|t ƒoLt|i i |i fgƒ}|d|d|gf}|ggf}nt ||fƒ‚|||fS(sÐ This method attempts to unify two terms. Two expressions are unifiable if there exists a substitution function S such that S(a) == S(-b). @param a: C{Expression} @param b: C{Expression} @param bindings: C{BindingDict} a starting set of bindings with which the unification must be consistent @return: C{BindingDict} A dictionary of the bindings required to unify @raise C{BindingException}: If the terms cannot be unified ii(R+t ExpressionR,R RRRbR7tmost_general_unificationR?RlR~RqRR}(RRmRZR[R‚RƒR„((s//p/zhu/06/nlp/nltk/nltk/inference/resolution.pyR|ds,  " "cCsp|dp |doEt|d|d||ƒ}|id|ƒ|i|ƒgSn|idƒgSdS(Niis -> New Clause: %ss -> End(RORzRs(R~RRZR[R\R]R)((s//p/zhu/06/nlp/nltk/nltk/inference/resolution.pyRVs   cCs3t|dƒ ot|ƒ o tgSngSdS(Ni(RR$(R~RRZR[R\R]((s//p/zhu/06/nlp/nltk/nltk/inference/resolution.pyRc˜s  cCs€g}xstt|ƒƒD]_}xI|iƒD];}t|iƒo%ttƒƒ}|i||ƒ}q,q,W|i|ƒqW|S(sC Skolemize, clausify, and standardize the variables apart. ( t _clausifyRRnt is_indvartnameR5tunique_variableRpR!(Rrt clause_listR>Rntnewvar((s//p/zhu/06/nlp/nltk/nltk/inference/resolution.pyR £s cCs^t|tƒot|iƒt|iƒSn$t|tƒoit|iƒ}t|iƒ}t|ƒdjpt‚t|ƒdjpt‚|d|dgSn«t|tƒot |gƒgSn‡t|t ƒot |gƒgSnct|t ƒoRt|i t ƒot |gƒgSqQt|i tƒot |gƒgSqQnt ƒ‚dS(s; @param expression: a skolemized expression in CNF iiN(R+t AndExpressionR‰R~Rt OrExpressionRR,RlROR7RbR?R(RrR~R((s//p/zhu/06/nlp/nltk/nltk/inference/resolution.pyR‰°s$RRcBsSeZed„Zd„Zd„Zd„Zd„Zd„Zd„Z d„Z RS(cCs9h|_|o%x"|D]\}}|||sR}cBseZd„ZRS(cCs<t|tƒoti|d|ƒnti||ƒdS(Ns'%s' cannot be bound to '%s'(R+ttuplet ExceptionR-(Rtarg((s//p/zhu/06/nlp/nltk/nltk/inference/resolution.pyR-Fs(RRR-(((s//p/zhu/06/nlp/nltk/nltk/inference/resolution.pyR}EstUnificationExceptioncBseZd„ZRS(cCsti|d||fƒdS(Ns'%s' cannot unify with '%s'(R¡R-(RRRm((s//p/zhu/06/nlp/nltk/nltk/inference/resolution.pyR-Ms(RRR-(((s//p/zhu/06/nlp/nltk/nltk/inference/resolution.pyR£LsRTcBs)eZedd„Zd„Zd„ZRS(icCs||_||_dS(N(tenabledtindent(RR¤R¥((s//p/zhu/06/nlp/nltk/nltk/inference/resolution.pyR-Rs cCst|i|i|ƒS(N(RTR¤R¥(RR&((s//p/zhu/06/nlp/nltk/nltk/inference/resolution.pyRkVscCs"|iod|i|GHndS(Ns (R¤R¥(RRz((s//p/zhu/06/nlp/nltk/nltk/inference/resolution.pyRzYs (RRR$R-RkRz(((s//p/zhu/06/nlp/nltk/nltk/inference/resolution.pyRTQs cCs˜tdƒtdƒtdƒtdƒtdƒtdƒtdƒtdƒtdƒtdƒtdƒtdƒtd ƒtd ƒtƒid ƒ}tƒid ƒ}tƒid ƒ}d|||tƒi|||gƒfGHtƒidƒ}tƒidƒ}tƒidƒ}d|||tƒi|||gƒfGHtƒidƒ}tƒidƒ}d||tƒi||gƒfGHdS(Nsman(x)s(man(x) -> man(x))s(man(x) -> --man(x))s-(man(x) and -man(x))s(man(x) or -man(x))s(man(x) iff man(x))s-(man(x) iff -man(x))s all x.man(x)s--all x.some y.F(x,y) & some x.all y.(-F(x,y))ssome x.all y.sees(x,y)sall x.(man(x) -> mortal(x))s man(Socrates)smortal(Socrates)s%s, %s |- %s: %ssall x.(man(x) -> walks(x))s man(John)ssome y.walks(y)s5some e1.some e2.(believe(e1,john,e2) & walk(e2,mary))ssome e0.walk(e0,mary)s %s |- %s: %s(tresolution_testt LogicParsertparseRR3(tp1tp2tctp((s//p/zhu/06/nlp/nltk/nltk/inference/resolution.pyttestResolutionProver^s2              **cCs7tƒi|ƒ}tƒi|ƒ}d||fGHdS(Ns |- %s: %s(R§R¨RR3(Rtftt((s//p/zhu/06/nlp/nltk/nltk/inference/resolution.pyR¦|scCsatƒ}t|idƒƒGHt|idƒƒGHt|idƒƒGHt|idƒƒGHt|idƒƒGHt|idƒƒGHt|idƒƒGHt|idƒƒGHt|id ƒƒGHt|id ƒƒGHt|id ƒƒGHt|id ƒƒGHt|id ƒƒGHt|idƒƒGHt|idƒƒGHt|idƒƒGHt|idƒƒGHdS(Ns P(x) | Q(x)s(P(x) & Q(x)) | R(x)sP(x) | (Q(x) & R(x))s(P(x) & Q(x)) | (R(x) & S(x))sP(x) | Q(x) | R(x)sP(x) | (Q(x) & R(x)) | S(x)sexists x.P(x) | Q(x)s-(-P(x) & Q(x))s P(x) <-> Q(x)s-(P(x) <-> Q(x))s -(all x.P(x))s-(some x.P(x))s some x.P(x)ssome x.all y.P(x,y)sall y.some x.P(x,y)sall z.all y.some x.P(x,y,z)s1all x.(all y.P(x,y) -> -all y.(Q(x,y) -> R(x,y)))(R§R R¨(tlp((s//p/zhu/06/nlp/nltk/nltk/inference/resolution.pyt test_clausifys$ cCs=tƒHtƒHtƒidƒ}t||gƒiƒGHdS(Nsman(x)(R±R­R§R¨RR3(R¬((s//p/zhu/06/nlp/nltk/nltk/inference/resolution.pytdemo›s t__main__N("t nltk.compatRtnltk.sem.logict nltk.sem.utilRtapiRRR¡RRRRRORUR{R R|RVRcR R‰tobjectRRRˆRžR}R£RTR­R¦R±R²R(((s//p/zhu/06/nlp/nltk/nltk/inference/resolution.pys s4 C?—  + \