QdhdZddlZddlmZddlmZddlmZmZddl m Z ddl m Z m Z mZmZmZmZmZmZmZmZmZGdd eZGd d eZGd d eZGddeZdZdZd&dZdZ dZ!dZ"dZ#GddZ$d'dZ%dZ&GddeZ'GddeZ(Gdd Z)d!Z*d"Z+d#Z,d$Z-e.d%kr e-dSdS)(z; Module for a resolution-based First Order theorem prover. N) defaultdict)reduce)BaseProverCommandProver) skolemize) AndExpressionApplicationExpressionEqualityExpression ExpressionIndividualVariableExpressionNegatedExpression OrExpressionVariableVariableExpression is_indvarunique_variableceZdZdS)ProverParseErrorN)__name__ __module__ __qualname__9lib/python3.11/site-packages/nltk/inference/resolution.pyrr"sDrrc$eZdZdZdZddZdZdS)ResolutionProverANSWERTNFc|sg}d} g}|r#|t| |D]$}|t|%||\}}|r'tt|nY#t $rL}|jr't| drd}g}n|rt|n|Yd}~nd}~wwxYw||fS)z :param goal: Input expression to prove :type goal: sem.Expression :param assumptions: Input expressions to use as assumptions in the proof :type assumptions: list(sem.Expression) Nz maximum recursion depth exceededF) extendclausify_attempt_proofprintResolutionProverCommand_decorate_clauses RuntimeError _assume_falsestr startswith)selfgoal assumptionsverboseresultclausesaes r_provezResolutionProver._prove*s. K G 0x///  , ,x{{++++"11'::OFG J-??HHIII   ! c!ff&7&72'' !HHHHG   sBB C."AC))C.ctt}d}|t|kr||s||r||ddz}n|dz}|t|kr||kr|r||s|||||||}|rA|D];}|dz|dzf|_||t|sd|fcSz.s0DD&SV--DDDDDDrA Tautology r4[z]  )maxr6r'ranger7r:)r.outmax_clause_len max_seq_lenr<parentstautseqs rr$z)ResolutionProverCommand._decorate_clausess9 DDGDDDDD#c'll++,, s7||$$ > >AGDqz&&(( #"qz" 3gaj122^c#gaj//.B.BBQFG'QGs3q1u::67#a!e**DC =s==gaj==7==T=== =CC r)NNN)F)rrrrDrKrV staticmethodr$rrrr#r#lsk        \rr#c^eZdZdZddZdZdZdZdZd Z d Z d Z d Z d Z dZdZdS)ClausecXt||d|_d|_dSrM)r5rD _is_tautologyr:)r)datas rrDzClause.__init__s) dD!!!! rNFc |t}|ggf}|ggf}t|trt|}t |||||t |}g}t |D]R\}} ||vrIt |D]9\} } || kr.| |vr*| | r|| :Sg} tt|D]!}||vr| ||"| S)a Attempt to unify this Clause with the other, returning a list of resulting, unified, Clauses. :param other: ``Clause`` with which to unify :param bindings: ``BindingDict`` containing bindings that should be used during the unification :param used: tuple of two lists 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: tuple of two ``Clause`` objects. 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: bool indicating whether debug statements should print :return: list containing all the resulting ``Clause`` objects that could be obtained by unification ) BindingDictrCbool DebugObject_iterate_first_complete_unify_path enumeratesubsumesr8rbr6) r)otherbindingsusedskippeddebugr>subsumedr<c1r=c2r-s rr9z Clause.unifys4&  "}}H <8D ?2hG eT " " '&&E# %42F  z** + +EAr  &z22++EArAvv!8"3"3 B"3 ***s:'' - -A   jm,,, rc|D] }||vrdS dS)z Return True iff every term in 'self' is a term in 'other'. :param other: ``Clause`` :return: bool FTr)r)rwr/s r isSubsetOfzClause.isSubsetOfs-  A~~uutrc Zg}|D]H}t|tr||j2|| It |}t }ggf}ggf}t d}tt|||||t|dkS)z 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: ``Clause`` :return: bool Fr) rCr r8rUrkrprrr6rs_subsumes_finalize) r)rw negatedotheratomnegatedotherClauserxryrzr{s rrvzClause.subsumess  + +D$ 122 +##DI....##TE****#L11==Bxr(E"" &&    rcTtt|||SrM)rkr5 __getslice__)r)startends rrzClause.__getslice__s"d''eS99:::rc:tfd|DS)Ncg|]}|v| Srr)rZr/rws r z"Clause.__sub__..s999Q!5..q...rrkr)rws `r__sub__zClause.__sub__s&9999$999:::rcRtt||SrM)rkr5__add__rs rrzClause.__add__sdll4//000rc|j|jSt|D]\}}t|tst |dz }||krh||}t|t r|j|kr d|_dSn*t|t r||jkr d|_dS|dz}||khd|_dS)z 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. Nr4TF)rmrurCr r6r rU)r)r<r/r=bs rr7zClause.is_tautologys   )% %dOO  DAqa!344 IIM!eeQA!!%677(6Q;;15D.#'44'$A'899(;;15D.#'44FA!ee#urcJttjd|DS)Nc3hK|]-}||zV.dSrM)free constants)rZrs rr[zClause.free..7s9$W$W$diikkDNN4D4D&D$W$W$W$W$W$Wr)roperatoror_r)s rrz Clause.free6s$hl$W$WRV$W$W$WXXXrc>tfd|DS)z Replace every instance of variable with expression across every atom in the clause :param variable: ``Variable`` :param expression: ``Expression`` c<g|]}|Sr)replace)rZr expressionvariables rrz"Clause.replace..As'KKKdt||Hj99KKKrr)r)rrs ``rrzClause.replace9s,KKKKKdKKKLLLrc:tfd|DS)z Replace every binding :param bindings: A list of tuples mapping Variable Expressions to the Expressions to which they are bound. :return: ``Clause`` c:g|]}|Sr)substitute_bindings)rZrrxs rrz.Clause.substitute_bindings..Ks'KKKdt//99KKKrr)r)rxs `rrzClause.substitute_bindingsCs(KKKKdKKKLLLrcLddd|DzdzS)N{, c3 K|] }d|zV dS)%sNr)rZitems rr[z!Clause.__str__..Ns&< New Clause: %sz -> End)rkrr)rrrxryrzr{r?s rrtrts Aw$q'71: 2U:VCDD  (94555--h7788 : rcTt|dst|sdgSgS)NrT)r6)rrrxryrzr{s rrrs/ wqz??3u:: v  rc*g}tt|D]s}|D]G}t|jr1t t }|||}H||t|S)zC Skolemize, clausify, and standardize the variables apart. ) _clausifyrrrnamerrrr8)r clause_listrTrnewvars rr r sKIj1122##KKMM 6 6D## 6+O,=,=>>f556"""" rct|tr)t|jt|jzSt|t rdt|j}t|j}t |dksJt |dksJ|d|dzgSt|trt|ggSt|trt|ggSt|trVt|j trt|ggSt|j trt|ggSt)z; :param expression: a skolemized expression in CNF r4r) rCrrrrrr6r rkr r rUr)rrrs rrrsd*m,,*)**Yz7H-I-III J - -***++:,--5zzQ6{{aa6!9$%% J 2 3 3* |$$%% J 5 6 6* |$$%% J 1 2 2* jo'< = = *J<(() )  ); < < *J<(() )   rc@eZdZd dZdZdZdZdZdZdZ d Z dS) rpNc6i|_|r |D] \}}|||< dSdS)z :param binding_list: list of (``AbstractVariableExpression``, ``AtomicExpression``) to initialize the dictionary Nd)r) binding_listvrs rrDzBindingDict.__init__sE  &  AQ    rct|tsJt|tsJ ||}n#t$rd}YnwxYw|r||kr ||j|<dSt|t r[ ||j}n#t$rd}YnwxYwt|}|r||kr||j|j<dStd|ztd|z)a A binding is consistent with the dict if its variable is not already bound, OR if its variable is already bound to its argument. :param variable: ``Variable`` The variable to bind :param binding: ``Expression`` The atomic to which 'variable' should be bound :raise BindingException: If the variable cannot be bound in this dictionary Nz*Variable %s already bound to another value) rCrr KeyErrorrr rrr)r)rbindingexistingbinding2s r __setitem__zBindingDict.__setitem__sA(H-----':..... H~HH   HHH  7h..&DF8    != > >   01    *(33H x833+3w'(((&CxP#?8L s!9 AA5 B BBct|tsJ|j|}|r% |j|}n#t$r|cYSwxYw|#dSdS)zD Return the expression to which 'variable' is bound N)rCrrr)r)r intermediates r __getitem__zBindingDict.__getitem__Cs(H-----vh'  $ $#vl3  $ $ $#### $ $ $ $ $ $s 6 AAc||jvSrMr)r)rs r __contains__zBindingDict.__contains__Pstv~rc t}|jD]}|j|||<|jD]}|j|||<|S#t$r}td|d|d|d}~wwxYw)a :param other: ``BindingDict`` The dict with which to combine self :return: ``BindingDict`` A new dict containing all the elements of both parameters :raise BindingException: If the parameter dictionaries are not consistent with each other z3Attempting to add two contradicting BindingDicts: 'z' and ''N)rprr)r)rwcombinedrr0s rrzBindingDict.__add__Ss "}}HV ( ("fQi W ) )#gaj O   ""15uuu>  sAA A,A''A,c*t|jSrM)r6rrs r__len__zBindingDict.__len__fs46{{rcdfdtjD}d|zdzS)Nrc3<K|]}|dj|VdS): Nr)rZrr)s rr[z&BindingDict.__str__..js7PPQ00TVAY00PPPPPPrrr)rsortedrkeys)r)data_strs` rrzBindingDict.__str__isJ99PPPP&:O:OPPPPPX~##rc d|zSrrrs rrzBindingDict.__repr__mrrrM) rrrrDrrrrrrrrrrrprps%%%N $ $ $&$$$rrpc|t}||kr|St|trt|||St|trt|||St|trLt|tr7t |j|j|t |j|j|zSt||f)ah Find the most general unification of the two given expressions :param a: ``Expression`` :param b: ``Expression`` :param bindings: ``BindingDict`` a starting set of bindings with which the unification must be consistent :return: a list of bindings :raise BindingException: if the Expressions cannot be unified ) rprCr _mgu_varr rrOrPr)r/rrxs rrrqs==Avv A3 4 4G1h''' A3 4 4G1h''' A, - -G*Q@U2V2VG' J H  $QZX F FG G Aq6 " ""rc|j||zvrt||ft |j|fg|zSrM)rrrrrp)varrrxs rrrsZ |z((:+?+?+A+AAAAZ0111S\:67888CCrceZdZdZdS)rct|tr t|d|zdSt||dS)Nz'%s' cannot be bound to '%s')rCtuple ExceptionrD)r)args rrDzBindingException.__init__sR c5 ! ! *   t%Cc%I J J J J J   tS ) ) ) ) )rNrrrrDrrrrrs#*****rrceZdZdZdS)UnificationExceptioncJt|d|d|ddS)Nrz' cannot unify with ')rrD)r)r/rs rrDzUnificationException.__init__s24!AQ!A!AQ!A!A!ABBBBBrNrrrrrrs(CCCCCrrc"eZdZddZdZdZdS)rrTrc"||_||_dSrM)enabledindent)r)rrs rrDzDebugObject.__init__s  rc<t|j|j|zSrM)rrrr)r)r<s rrzDebugObject.__add__s4<q999rcL|jrtd|jz|zdSdS)Nz )rr"r)r)rs rrzDebugObject.lines6 < / &4;&- . . . . . / /rN)Tr)rrrrDrrrrrrrrrsF::://///rrrc Jtdtdtdtdtdtdtdtdtdtdtdtdtd td tjd }tjd }tjd }t|d|d|dt |||gtjd}tjd}tjd}t|d|d|dt |||gtjd}tjd}t|d|dt ||gdS)Nman(x)z(man(x) -> man(x))z(man(x) -> --man(x))z-(man(x) and -man(x))z(man(x) or -man(x))z(man(x) iff man(x))z-(man(x) iff -man(x))z all x.man(x)z--all x.some y.F(x,y) & some x.all y.(-F(x,y))zsome x.all y.sees(x,y)zall x.(man(x) -> mortal(x))z man(Socrates)zmortal(Socrates)rz |- rzall x.(man(x) -> walks(x))z man(John)zsome y.walks(y)z5some e1.some e2.(believe(e1,john,e2) & walk(e2,mary))zsome e0.walk(e0,mary))resolution_testr fromstringr"rrK)p1p2cps rtestResolutionProverrs*I)***+,,,,---*+++)***,---*+++)****+++,---N###CDDD,---  = > >B  / 0 0B122A R G G2 G G1 G G 0 2 2 8 8RH E E G GHHH  < = =B  | , ,B011A R G G2 G G1 G G 0 2 2 8 8RH E E G GHHHVWWA677A Q ; ;A ; ;)++11!aS99 ; ;<<<< Q(x)z-(P(x) <-> Q(x))z -(all x.P(x))z-(some x.P(x))z some x.P(x)zsome x.all y.P(x,y)zall y.some x.P(x,y)zall z.all y.some x.P(x,y,z)z1all x.(all y.P(x,y) -> -all y.(Q(x,y) -> R(x,y))))r rr"r )lexprs r test_clausifyr s=  !E (55'' ( ())) (55/00 1 1222 (55/00 1 1222 (55899 : :;;; (55-.. / /000 (55677 8 8999 (55/00 1 1222 (55*++ , ,--- (55)) * *+++ (55+,, - -... (55)) * *+++ (55)** + +,,, (55'' ( ())) (55.// 0 0111 (55.// 0 0111 (55677 8 8999 (55LMM N NOOOOOrctttttjd}tt ||gdS)Nr)r r"rr rr#rK)rs rdemor sfOOO GGG GGGh''A !!aS ) ) / / 1 122222r__main__)NNrM)/__doc__r collectionsr functoolsrnltk.inference.apirrnltk.semrnltk.sem.logicrr r r r r rrrrrrrrr#r5rkrsrrrtrr rrprrrrrrrrr r rrrrrsU######88888888                               y   C C C C C vC C C L?????/???DcccccTcccL)))X$$$N+(+(+(+(\      0]]]]]]]]@####6DDD*****y***CCCCC9CCC / / / / / / / /===> PPP4333 zDFFFFFr