OffcSrSSKrSSKrSSKrSSKrSSKJr SSKJr SSK J r J r J r J r JrJrJrJrJrJrJrJrJrJrJrJr "SS\5r"SS \5rS rS rS rS r "SS\!5r"\RF"S5r$\RF"S5r%\RF"S\RL5r'Sr(S"Sjr)"SS\!5r*"SS5r+Sr,S"Sjr-S#Sjr.S"Sjr/S"Sjr0S$Sjr1\2S:Xa\1"S SS!9 gg)%zK This module provides data structures for representing first-order models. Npformat) decorator)AbstractVariableExpression AllExpression AndExpressionApplicationExpressionEqualityExpressionExistsExpression Expression IffExpression ImpExpressionIndividualVariableExpressionIotaExpressionLambdaExpressionNegatedExpression OrExpressionVariable is_indvarc\rSrSrSrg)Error,N__name__ __module__ __qualname____firstlineno____static_attributes__r3/usr/lib/python3/dist-packages/nltk/sem/evaluate.pyrr,r rc\rSrSrSrg) Undefined0rNrrr r!r$r$0r"r r$c[R"U5n[[USU55nUR SS5(a/[ 5 UR 5Hn[ SU-5 M U"U0UD6$)Nrtracez%s => %s)inspectgetfullargspecdictzippopprintitems)fargskwargspecditems r!r'r'4sh$$Q'G ST "#AuuWd GGID *t# $ d>b>r c[U5S:Xag[SU55(a+[[U55[[U55:Xag[ SU-5e)z Check whether a set represents a relation (of any arity). :param s: a set containing tuples of str elements :type s: set :rtype: bool rTc3B# UHn[U[5v M g7fN) isinstancetuple).0els r! is_rel..Js /QrZE " "Qsz.Set %r contains sequences of different lengths)lenallmaxmin ValueError)ss r!is_relrD>sN 1v{ /Q / / /CAK3s1v;4NIAMNNr c[5nUHnn[U[5(aURU45 M,[U[5(aUR[U55 M]URU5 Mp U$)a. Convert a set containing individuals (strings or numbers) into a set of unary tuples. Any tuples of strings already in the set are passed through unchanged. For example: - set(['a', 'b']) => set([('a',), ('b',)]) - set([3, 27]) => set([('3',), ('27',)]) :type s: set :rtype: set of tuple of str )setr8straddint)rCnewelems r!set2relrLPs_ %C dC GGTG  c " " GGCI  GGDM  Jr cP[U5S:Xag[[U5S5$)zU Check the arity of a relation. :type rel: set of tuples :rtype: int of tuple of str r)r>list)rels r!arityrPhs%  3x1} tCy| r ch^\rSrSrSrU4SjrSrSr\S5r \S5r \ S5r S r U=r$) Valuationsa A dictionary which represents a model-theoretic Valuation of non-logical constants. Keys are strings representing the constants to be interpreted, and values correspond to individuals (represented as strings) and n-ary relations (represented as sets of tuples of strings). An instance of ``Valuation`` will raise a KeyError exception (i.e., just behave like a standard dictionary) if indexed with an expression that is not in its list of symbols. c,>[TU]5 UHup#[U[5(d[U[5(aX0U'M5[U[ 5(a[ U5X'MY[R"SU<SU<3SS9n[U5e g)z- :param xs: a list of (symbol, value) pairs. z@Error in initializing Valuation. Unrecognized value for symbol 'z': B)widthN) super__init__r8rGboolrFrLtextwrapfillrB)selfxssymvalmsg __class__s r!rXValuation.__init__s| HC#s##z#t'<'<S C%%#CL mmADcK !o%r cRX;a[RX5$[SU-5e)NzUnknown expression: '%s'r* __getitem__r$r\keys r!reValuation.__getitem__s) ;##D. .6<= =r c[U5$r7rr\s r!__str__Valuation.__str__s t}r c 6/nUR5Hsn[U[5(aURU5 M+[U[5(aMBUR UVVs/sHo3H oDcMUPM M snn5 Mu [ U5$s snnf)z7Set-theoretic domain of the value-space of a Valuation.)valuesr8rGappendrYextendrF)r\domr_tuple_rKs r!domainValuation.domainsu;;=C#s## 3T** (+SfTTS !3xTs % B 4 B c4[UR55$)z9The non-logical constants which the Valuation recognizes.)sortedkeysrjs r!symbolsValuation.symbolssdiik""r c[U5$r7)read_valuation)clsrCs r! fromstringValuation.fromstrings a  r r)rrrr__doc__rXrerkpropertyrsrx classmethodr}r __classcell__ras@r!rRrRssS &&>   ##!!r rRz \s*=+>\s*z\s*,\s*zg\s* (\([^)]+\)) # tuple-expression \s*ct[RU5nUSnUSnURS5(aUSSn[R U5nU(a@/nUH7nUSSn[ [ RU55nURU5 M9 O[ RU5n[U5nX#4$)z Read a line in a valuation file. Lines are expected to be of the form:: noosa => n girl => {g1, g2} chase => {(b1, g1), (b2, g1), (g1, d1), (g2, d2)} :param s: input line :type s: str :return: a pair (symbol, value) :rtype: tuple r{) _VAL_SPLIT_REsplit startswith _TUPLES_REfindallr9_ELEMENT_SPLIT_RErorF)rCpiecessymbolvalue tuple_strings set_elementstselements r!_read_valuation_liners  #F AYF 1IE a "**51 L#"X 1 7 7 ;<##G,$ -2259LL! =r cbUbURU5n/n[UR55HNup4UR5nUR S5(dUS:XaM3UR [ U55 MP [U5$![an[SUSU35UeSnAff=f)z Convert a valuation string into a valuation. :param s: a valuation string :type s: str :param encoding: the encoding of the input string, if it is binary :type encoding: str :return: a ``nltk.sem`` valuation :rtype: Valuation N#zUnable to parse line z: ) decode enumerate splitlinesstriprrorrBrR)rCencoding statementslinenumlinees r!r{r{s HHX J"1<<>2 zz| ??3  42:  O   248 9 3 Z   O4WIRvFGQ N Os$B  B.B))B.cX^\rSrSrSrS U4SjjrSrSrS SjrSr Sr S r S r U=r $) Assignmenta A dictionary which represents an assignment of values to variables. An assignment can only assign values from its domain. If an unknown expression *a* is passed to a model *M*\ 's interpretation function *i*, *i* will first check whether *M*\ 's valuation assigns an interpretation to *a* as a constant, and if this fails, *i* will delegate the interpretation of *a* to *g*. *g* only assigns values to individual variables (i.e., members of the class ``IndividualVariableExpression`` in the ``logic`` module. If a variable is not assigned a value by *g*, it will raise an ``Undefined`` exception. A variable *Assignment* is a mapping from individual variables to entities in the domain. Individual variables are usually indicated with the letters ``'x'``, ``'y'``, ``'w'`` and ``'z'``, optionally followed by an integer (e.g., ``'x0'``, ``'y332'``). Assignments are created using the ``Assignment`` constructor, which also takes the domain as a parameter. >>> from nltk.sem.evaluate import Assignment >>> dom = set(['u1', 'u2', 'u3', 'u4']) >>> g3 = Assignment(dom, [('x', 'u1'), ('y', 'u2')]) >>> g3 == {'x': 'u1', 'y': 'u2'} True There is also a ``print`` format for assignments which uses a notation closer to that in logic textbooks: >>> print(g3) g[u1/x][u2/y] It is also possible to update an assignment using the ``add`` method: >>> dom = set(['u1', 'u2', 'u3', 'u4']) >>> g4 = Assignment(dom) >>> g4.add('x', 'u1') {'x': 'u1'} With no arguments, ``purge()`` is equivalent to ``clear()`` on a dictionary: >>> g4.purge() >>> g4 {} :param domain: the domain of discourse :type domain: set :param assign: a list of (varname, value) associations :type assign: list c>[TU]5 XlU(aYUHSup4X@R;d!SRUUR55e[ U5(d SU-5eX@U'MU SUlUR 5 g)Nz'{}' is not in the domain: {}-Wrong format for an Individual Variable: '%s')rWrXrsformatrvariant _addvariant)r\rsassignvarr_ras r!rXAssignment.__init__0s  "kk)+J+Q+QKK,)!~~CcI~ S #  r cRX;a[RX5$[SU-5e)Nz"Not recognized as a variable: '%s'rdrfs r!reAssignment.__getitem__@s) ;##D. .@3FG Gr cR[UR5nURU5 U$r7)rrsupdate)r\rJs r!copyAssignment.copyFs!% 4 r cXU(aX OUR5 UR5 g)z Remove one or all keys (i.e. logic variables) from an assignment, and update ``self.variant``. :param var: a Variable acting as a key for the assignment. N)clearr)r\rs r!purgeAssignment.purgeKs$  JJL r cbSn[UR5nUHup4USUSUS3- nM U$)zA Pretty printing for assignments. {'x', 'u'} appears as 'g[u/x]' g[/])rvr)r\gstringrr_rs r!rkAssignment.__str__YsA&HC 3%qQ' 'G r cx/nUR5HnUSUS4nURU5 M Xlg)z; Create a more pretty-printable version of the assignment. rrN)r.ror)r\list_r4pairs r!rAssignment._addvariantdsAJJLDGT!W%D LL ! r cX R;dUSUR35e[U5(d SU-5eX U'UR5 U$)zP Add a new variable-value pair to the assignment, and update ``self.variant``. z is not in the domain r)rsrr)r\rr_s r!rHAssignment.addos[ kk!NcU*@ #NN!~~TNQTTT~S   r )rsrr7)rrrrrrXrerrrkrrHrrrs@r!rrs22h H      r rcR\rSrSrSrSrSrSrS SjrS Sjr S S jr SS jr S r g)Modeli|a/ A first order model is a domain *D* of discourse and a valuation *V*. A domain *D* is a set, and a valuation *V* is a map that associates expressions with values in the model. The domain of *V* should be a subset of *D*. Construct a new ``Model``. :type domain: set :param domain: A set of entities representing the domain of discourse of the model. :type valuation: Valuation :param valuation: the valuation of the model. :param prop: If this is set, then we are building a propositional model and don't require the domain of *V* to be subset of *D*. c[U[5(deXlX lUR UR5(d[ SUR<SU<35eg)NzThe valuation domain, z*, must be a subset of the model's domain, )r8rFrs valuation issupersetr)r\rsrs r!rXModel.__init__sX&#&&&& "  !1!122##V- 3r c@SUR<SUR<S3$)N(z, )rsrrjs r!__repr__Model.__repr__s 4;;/DNN#5Q77r c:SURSUR3$)Nz Domain = z, Valuation = rrjs r!rk Model.__str__s4;;-'88HIIr Nc[R"U5nURXBUS9nU(a[5 [SUSUSU35 U$![a% U(a[5 [SUSU35 gf=f)a  Read input expressions, and provide a handler for ``satisfy`` that blocks further propagation of the ``Undefined`` error. :param expr: An ``Expression`` of ``logic``. :type g: Assignment :param g: an assignment to individual variables. :rtype: bool or 'Undefined' r''z' evaluates to z under M, z' is undefined under M, r$)r r}satisfyr-r$)r\exprrr'parsedrs r!evaluateModel.evaluates **40FLL%L8E$ugZsCDL $7s;<  sA A,A>=A>c ^^[U[5(aUR5upE[U[5(a,TR UT5n[ UU4SjU55nXv;$TR UR T5nTR URT5nXh$[U[5(a!TR URT5(+$[U[5(a?TR URT5=(a TR URT5$[U[5(a?TR URT5=(d TR URT5$[U[5(aDTR URT5(+=(d TR URT5$[U[5(a9TR URT5TR URT5:H$[U[ 5(a9TR URT5TR URT5:H$[U["5(amTR%5n TR&HLn U R)UR*R,U 5 TR URU 5(aML g g[U[.5(amTR%5n TR&HLn U R)UR*R,U 5 TR URU 5(dML g g[U[05(amTR%5n TR&HLn U R)UR*R,U 5 TR URU 5(dML g g[U[25(a\0n UR*R,n TR&H2n TR URTR)X55n XU 'M4 U $TR5UTU5$)a Recursive interpretation function for a formula of first-order logic. Raises an ``Undefined`` error when ``parsed`` is an atomic string but is not a symbol or an individual variable. :return: Returns a truth value or ``Undefined`` if ``parsed`` is complex, and calls the interpretation function ``i`` if ``parsed`` is atomic. :param parsed: An expression of ``logic``. :type g: Assignment :param g: an assignment to individual variables. c3H># UHnTRUT5v M g7fr7)r)r:argrr\s r!r< Model.satisfy..sJ  S! 4 4 s"FT)r8r uncurryrrr9functionargumentrtermrfirstsecondrrr r rrrsrHvariablenamer rri)r\rrr'r argumentsfunvalargvalsargvalnew_gucfrr_s` ` r!r Model.satisfysI f3 4 4"(.."2 H($>??h2J JJ((fooq9fooq9~%  1 2 2||FKK33 3  . .<< a0ST\\&--QR5S S  - -<< a0RDLLPQ4R R  . . V\\155X$,,v}}VW:X X  . .<< a0DLLPQ4RR R  2 3 3<< a0DLLPQ4RR R  . .FFHE[[ &//..2||FKK77 !  0 1 1FFHE[[ &//..2<< U33!  / /FFHE[[ &//..2<< U33!  0 1 1B//&&C[[ll6;;c > 1 !I66&!U+ +r cURRURR;a#URURR$[ U[ 5(aX!RR$[ SU-5e)ax An interpretation function. Assuming that ``parsed`` is atomic: - if ``parsed`` is a non-logical constant, calls the valuation *V* - else if ``parsed`` is an individual variable, calls assignment *g* - else returns ``Undefined``. :param parsed: an ``Expression`` of ``logic``. :type g: Assignment :param g: an assignment to individual variables. :return: a semantic value zCan't find a value for %s)rrrrxr8rr$)r\rrr's r!rModel.ism$ ??  4>>#9#9 9>>&//"6"67 7  < = =__))* *7&@A Ar c SnXfU--n/n[U[5(a [U5n OUn XR5;GaU(a [ 5 [ Xe-SUSU3-5 UR Hn UR 5n U RU RU 5 U(a US:aUS- n OSn URXU 5n U(a[ USU --5 U S:Xa U(a[ USUS U S 3-5 MMURU 5 U(dM[ USUS U S U 3-5 M UVs1sHoiM nnU$[U RS U35es snf) a] Generate the entities from the model's domain that satisfy an open formula. :param parsed: an open formula :type parsed: Expression :param varex: the relevant free individual variable in ``parsed``. :type varex: VariableExpression or str :param g: a variable assignment :type g: Assignment :return: a set of the entities that satisfy ``parsed``. z zOpen formula is 'z' with assignment rrz(trying assignment %s)Fz value of 'z' under z is Falsez is z is not free in ) r8rGrfreer-rsrrHrrror$)r\rvarexrr'nestingspacerindent candidatesrrrlowtracercresults r! satisfiersModel.satisfiersszG+, eS ! !5/CC ++- %)&1CA3GH[[ #((A&UQY$qyH H VH=&#;e#CCDE>fF88E7)'TTU %%a(ufF88E7$ug'VVW+!.",,AaF,  sxxj(8AB B-s E,rr7)F)Nr) rrrrrrXrrkrrrrrrr r!rr|s."8J,I,XB49r rc  [/SQ5q[5q[ [[5q[ [5q[5 [S[-5 [S5 [S[-5 [S5 [5 [S[ 5 [S[-5 /SQnUHZnU(a'[5 [ RU[U5 M1[SUS[ RU[535 M\ g ) z!Example of a propositional model.))PT)QT)RF*zPropositional Formulas Demoz7(Propositional constants treated as nullary predicates)z Model m1: )z(P & Q)z(P & R)z- Pz- Rz- - Pz - (P & R)z(P | R)z(R | P)z(R | R)z (- P | R)z (P | - P)z(P -> Q)z(P -> R)z(R -> P)z (P <-> P)z (R <-> R)z (P <-> R)The value of '' is: N) rRval1rFdom1rm1rg1r-multr)r' sentencessents r!propdemor _s = >D 5D tT B D B G #* '( #* CD G - #*I(  G KKb% ( N4&r{{4/D.EF G r c SSSSSS14SSS 14S S 14S 1S k4/q[[5q[Rq[ [[5q[[SS/5qU(Gd*[5 [S[-5 [S5 [S[-5 [SSS[ 5 [S[5 /SQnUVs/sHn[R"U5PM nn[5 UH/n[SU<S[ RU[5<35 M1 /SQnUH[upx[ R[R"U5[5n [SU55n [USUSX;35 M] ggs snf![a [SU-5 Mf=f![a [USUS35 Mf=f) zExample of a first-order model.)adamb1)bettyr)fidod1girlrg2boyrb2dogrlove>rrrrrrrr)xr)yrrz Models Demoz Model m2: z-------------- zVariable assignment = )rrrwalksrrzzThe interpretation of 'z ' in m2 is z-The interpretation of '%s' in m2 is Undefined))rr)r )r)r)rr)r)rrc3~# UH3n[R[R"U5[5v M5 g7fr7)m2rr r}r)r:rs r!r<folmodel..s+UPTZ%:%:3%? D DPTs;=rz) evaluates to z) evaluates to UndefinedN)v2rRval2rsdom2rr#rrr-r r r}rr$r9) quietr'exprsr parsed_exprsr applicationsfunr0rargsvals r!folmodelr.s  $ t   IJ B R=D ;;D tT B D; 4 5B   cDj m cDj mXtR0 &+?:?@%Q --a0% @ "F PrttFB/1# &IC ?j33C8"=UPTUUQtfOG4E3FGH &9 A PENO P ?Qtf$<=> ?s+ F;+F6AF5F21F25GGc d[SS9 [5 [S[-5 [S5 [S[-5 /SQnUHdn[R 5 U(a[ R U[U5 M;[SUS[ R U[535 Mf g) z> Interpretation of closed expressions in a first-order model. Tr(rzFOL Formulas Demo)zlove (adam, betty)z (adam = mia)z\x. (boy(x) | girl(x))z\x. boy(x)(adam)z\x y. love(x, y)z\x y. love(x, y)(adam)(betty)z\x y. love(x, y)(adam, betty)z\x y. (boy(x) & love(x, y))z#\x. exists y. (boy(x) & love(x, y))zexists z1. boy(z1)z!exists x. (boy(x) & -(x = adam))z&exists x. (boy(x) & all y. love(y, x))zall x. (boy(x) | girl(x))z1all x. (girl(x) -> exists y. boy(y) & love(x, y))z3exists x. (boy(x) & all y. (girl(y) -> love(y, x)))z3exists x. (boy(x) & all y. (girl(y) -> love(x, y)))zall x. (dog(x) -> - girl(x))z-exists x. exists y. (love(x, y) & love(x, y))rrN)r.r-r rrr#r)r'formulasfmlas r!foldemor3s 4 G #*  #*H*   KKb% ( N4&r{{4/D.EF G r c  [5 [S[-5 [S5 [S[-5 [SS9 /SQnU(a[[5 UH$n[U5 [R "U5 M& UVs/sHn[R "U5PM nnUHLn[ R5 [SRU[RUS[ U555 MN gs snf) z5Satisfiers of an open formula in a first order model.rzSatisfiers DemoTr0)zboy(x)z(x = x)z(boy(x) | girl(x))z(boy(x) & girl(x))z love(adam, x)z love(x, adam)z -(x = adam)zexists z22. love(x, z22)exists y. love(y, x)zall y. (girl(y) -> love(x, y))zall y. (girl(y) -> love(y, x))z)all y. (girl(y) -> (boy(x) & love(y, x)))z)(boy(x) & all y. (girl(y) -> love(x, y)))z)(boy(x) & all y. (girl(y) -> love(y, x)))z+(boy(x) & exists y. (girl(y) & love(y, x)))z(girl(x) -> dog(x))zall y. (dog(y) -> (x = y))r5z&exists y. (love(adam, y) & love(y, x))zThe satisfiers of '{}' are: {}rN) r-r r.r#r r}rrrr)r'r1r2rps r!satdemor7s G #*  #* 4H,  b  d d#7? ?hdj##D)hF ?    , 3 3Ar}}QRQV7W X @s Dc[[[[S.nX "US9 g![a UH nX "US9 M gf=f)a/ 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 )rrN)r r.r3r7KeyError)numr'demoss r!demor?(sDX'g >E$  $C JU #$s"AA__main__r9rr7)FN)rN)3rr(resysrZpprintrnltk.decoratorsrnltk.sem.logicrrrr r r r r rrrrrrrr Exceptionrr$r'rDrLrPr*rRcompilerrVERBOSErrr{rrr r r.r3r7r?rrr r!rIs  %( I   O$0<!<!D <( JJz* ZZ'JJ   F!2~~BWW|  *Hb5?x%HX- `$* z!r