³ò ’B_Kc @sodZddklZddkZddkZddklZddklZddk Tde fd„ƒYZ d e fd „ƒYZ d „Z d „Zd „Zd„Zedƒed„ƒZdefd„ƒYZdefd„ƒYZdefd„ƒYZdZdd„Zedd„Zdd„Zdd„Zddd„Zedjoedd dƒndS(!sL This module provides data structures for representing first-order models. iÿÿÿÿ(tpformatN(t decorator(t deprecated(t*tErrorcBseZRS((t__name__t __module__(((s'/p/zhu/06/nlp/nltk/nltk/sem/evaluate.pyRst UndefinedcBseZRS((RR(((s'/p/zhu/06/nlp/nltk/nltk/sem/evaluate.pyRscOsmti|ƒ}tt|d|ƒƒ}|iddƒo%Hx!|iƒD]}d|GHqIWn|||ŽS(Nittraces%s => %s(tinspectt getargspectdicttziptpoptNonetitems(tftargstkwtargspectdtitem((s'/p/zhu/06/nlp/nltk/nltk/sem/evaluate.pyR s cCs›t|ƒdjotSn}|tg}|D]!}t|tƒo ||q,q,~ƒjo-tt|ƒƒtt|ƒƒjotSntd|‚dS(s¬ Check whether a set represents a relation (of any arity). @param s: a set containing C{tuple}s of C{str} elements @type s: C{set} @rtype: C{bool} is.Set %r contains sequences of different lengthsN(tlentTruetsett isinstancettupletmaxtmint ValueError(tst_[1]telem((s'/p/zhu/06/nlp/nltk/nltk/sem/evaluate.pytis_rel)s B%cCsvtƒ}xf|D]^}t|tƒo|i|fƒqt|tƒo|it|ƒƒq|i|ƒqW|S(sj Convert a set containing individuals (strings or numbers) into a set of unary tuples. Any tuples of strings already in the set are passed through unchanged. For example: - set(['a', 'b']) => set([('a',), ('b',)]) - set([3, 27]) => set([('3',), ('27',)]) @type s: C{set} @rtype: C{set} of C{tuple} of C{str} (RRtstrtaddtint(RtnewR ((s'/p/zhu/06/nlp/nltk/nltk/sem/evaluate.pytset2rel;s cCs/t|ƒdjodSntt|ƒdƒS(st Check the arity of a relation. @type rel: C{set} of C{tuple}s @rtype: C{int} of C{tuple} of C{str} i(Rtlist(trel((s'/p/zhu/06/nlp/nltk/nltk/sem/evaluate.pytarityRssSimply use 'args in rel'cCst|ƒpt‚||jS(s¸ Apply a relation (as set of tuples) to an argument. @type rel: C{set} of C{tuple}s @param args: a sequence of appropriate semantic arguments @rtype: C{bool} (R!tAssertionError(R(RR((s'/p/zhu/06/nlp/nltk/nltk/sem/evaluate.pytapp\s t ValuationcBs_eZdZd„Zd„Zd„Zd„ZeeddƒZd„Z ee ddƒZ RS( sâ A dictionary which represents a model-theoretic Valuation of non-logical constants. Keys are strings representing the constants to be interpreted, and values correspond to individuals (represented as strings) and n-ary relations (represented as sets of tuples of strings). An instance of L{Valuation} will raise a KeyError exception (i.e., just behave like a standard dictionary) if indexed with an expression that is not in its list of symbols. cCs¥ti|ƒx‘|D]‰\}}t|tƒpt|tƒo|||tpropertytdomainRBtsymbols(((s'/p/zhu/06/nlp/nltk/nltk/sem/evaluate.pyR,is        t AssignmentcBsSeZdZed„Zd„Zd„Zed„Zd„Zd„Z d„Z RS(s‡ A dictionary which represents an assignment of values to variables. An assigment can only assign values from its domain. If an unknown expression M{a} is passed to a model M{M}'s interpretation function M{i}, M{i} will first check whether M{M}'s valuation assigns an interpretation to M{a} as a constant, and if this fails, M{i} will delegate the interpretation of M{a} to M{g}. M{g} only assigns values to individual variables (i.e., members of the class L{IndividualVariableExpression} in the L{logic} module. If a variable is not assigned a value by M{g}, it will raise an C{Undefined} exception. cCs’ti|ƒ||_|ogxd|D]X\}}||ijptd||if‚t|ƒptd|‚|||Îss%s is not free in %s( RR"tVariabletfreeRERMR#RpRZRqR;RR(R2R]tvarexRPRtnestingtspacertindentt candidatesRKR{RztlowtraceR^tresult((s'/p/zhu/06/nlp/nltk/nltk/sem/evaluate.pyt satisfierss:      ( RRRCR.RWR9RR_RZRqRtR‰(((s'/p/zhu/06/nlp/nltk/nltk/sem/evaluate.pyRTþs     J icCstdtfdtfdtfgƒatgƒatttƒattƒa Hdt GHdGHdt GHdGHHdGtGHdt GHdd d d d d dddddddddddg}xH|D]@}|oHti |t |ƒq¾d|ti |t ƒfGHq¾WdS(s!Example of a propositional model.tPtQtRRsPropositional Formulas Demos7(Propositional constants treated as nullary predicates)s Model m1: s(P & Q)s(P & R)s- Ps- Rs- - Ps - (P & R)s(P | R)s(R | P)s(R | R)s (- P | R)s (P | - P)s(P -> Q)s(P -> R)s(R -> P)s (P <-> P)s (R <-> R)s (P <-> R)sThe value of '%s' is: %sN( R,RRqtval1Rtdom1RTtm1RGtg1tmultR_(Rt sentencestsent((s'/p/zhu/06/nlp/nltk/nltk/sem/evaluate.pytpropdemoásF'       c s1ddd dtddgƒfd tdd gƒfd tdgƒfd td!d"d#d$gƒfgattƒatiatttƒattd%d&gƒa |p‡Hdt GHdGHdt GHdGd'GdGtGHdGt GHdd d dd ddg}t ƒ‰g}|D]}|ˆi |ƒq~}HxL|D]D}yd|ti |t ƒfGHWq.tj od|GHq.Xq.Wd(dd)fd d*fd d+fg}x|D]„\}} ySti ˆi |ƒt ƒ} t‡fd†| Dƒƒ} d|| | | jfGHWq¡tj od|| fGHq¡Xq¡WndS(,sExample of a first-order model.tadamtb1tbettyRtfidotd1tgirltg2tboytb2tdogtlovetxtyRs Models Demos Model m2: t-is sVariable assignment = twalkstzs&The interpretation of '%s' in m2 is %ss-The interpretation of '%s' in m2 is Undefinedc3s.x'|] }tiˆi|ƒtƒVqWdS(N(tm2RtRYR›(R~Rw(R\(s'/p/zhu/06/nlp/nltk/nltk/sem/evaluate.pys 6ss%s(%s) evaluates to %ss%s(%s) evaluates to UndefinedN(R•sb1(R—sg1(sfidosd1(sb1sg1(sb2sg2(sg1sb1(sg2sb1(R sb1(R¡sg2s--------------(sboyR•(R•(R•R¡(R¡R•(Rtv2R,tval2REtdom2RTR¥RGR›R‘RXRYRtRR( tquietRtexprsRtet parsed_exprsR]t applicationstfunRRvtargsval((R\s'/p/zhu/06/nlp/nltk/nltk/sem/evaluate.pytfolmodelsB <!      *$ cCs¹tdtƒHdtGHdGHdtGHdddddd d d d d ddddddddg}xQ|D]I}tiƒ|oti|t|ƒqhd|ti|tƒfGHqhWdS(sF Interpretation of closed expressions in a first-order model. R©RsFOL Formulas Demoslove (adam, betty)s (adam = mia)s\x. (boy(x) | girl(x))s\x. boy(x)(adam)s\x y. love(x, y)s\x y. love(x, y)(adam)(betty)s\x y. love(x, y)(adam, betty)s\x y. (boy(x) & love(x, y))s#\x. exists y. (boy(x) & love(x, y))sexists z1. boy(z1)s!exists x. (boy(x) & -(x = adam))s&exists x. (boy(x) & all y. love(y, x))sall x. (boy(x) | girl(x))s1all x. (girl(x) -> exists y. boy(y) & love(x, y))s3exists x. (boy(x) & all y. (girl(y) -> love(y, x)))s3exists x. (boy(x) & all y. (girl(y) -> love(x, y)))sall x. (dog(x) -> - girl(x))s-exists x. exists y. (love(x, y) & love(x, y))sThe value of '%s' is: %sN(R°RR‘R›ROR¥R_(Rtformulastfmla((s'/p/zhu/06/nlp/nltk/nltk/sem/evaluate.pytfoldemo>s:     cCs HdtGHdGHdtGHtdtƒdddddd d d d d dddddddd dg}|o tGHntƒ}x |D]}|GH|i|ƒq„Wg}|D]}||i|ƒq«~}x9|D]1}tiƒd|ti|dt|ƒfGHqÑWdS(s5Satisfiers of an open formula in a first order model.RsSatisfiers DemoR©sboy(x)s(x = x)s(boy(x) | girl(x))s(boy(x) & girl(x))s love(adam, x)s love(x, adam)s -(x = adam)sexists z22. love(x, z22)sexists y. love(y, x)sall y. (girl(y) -> love(x, y))sall y. (girl(y) -> love(y, x))s)all y. (girl(y) -> (boy(x) & love(y, x)))s)(boy(x) & all y. (girl(y) -> love(x, y)))s)(boy(x) & all y. (girl(y) -> love(y, x)))s+(boy(x) & exists y. (girl(y) & love(y, x)))s(girl(x) -> dog(x))sall y. (dog(y) -> (x = y))s&exists y. (love(adam, y) & love(y, x))sThe satisfiers of '%s' are: %sR N( R‘R°RR¥RXRYR›ROR‰(RR±R\R²RR]tp((s'/p/zhu/06/nlp/nltk/nltk/sem/evaluate.pytsatdemojsH      * icCs{htd<td<td<td<}y||d|ƒWn5tj o)x$|D]}||d|ƒqWWnXdS(sO Run exists demos. - num = 1: propositional logic demo - num = 2: first order model demo (only if trace is set) - num = 3: first order sentences demo - num = 4: satisfaction of open formulas demo - any other value: run all the demos @param trace: trace = 1, or trace = 2 for more verbose tracing iiiiRN(R”R°R³RµtKeyError(tnumRtdemos((s'/p/zhu/06/nlp/nltk/nltk/sem/evaluate.pytdemo™s     t__main__iR( RCtpprintRR R0tnltk.decoratorsRtnltk.internalsRtlogict ExceptionRRRR!R&R)RqR+R R,RGtobjectRTR‘RR”R°R³RµR¹R(((s'/p/zhu/06/nlp/nltk/nltk/sem/evaluate.pyss2       7^ß /. , /