+ hfcRt^RIt^RIt^RIt^RIt^RIHt^RIHt^RI H t H t H t H t HtHtHtHtHtHtHtHtHtHtHtHt!RR]4t!RR]4tR tR tR tR t !R R]!4t"]PF!R4t$]PF!R4t%]PF!R]PL4t'Rt(RRlt)!RR]!4t*!RR4t+^t,RRlt-R Rlt.RRlt/RRlt0R!Rlt1]2R8Xd ]1!^^R7R#R#)"zK This module provides data structures for representing first-order models. Npformat) decorator)AbstractVariableExpression AllExpression AndExpressionApplicationExpressionEqualityExpressionExistsExpression Expression IffExpression ImpExpressionIndividualVariableExpressionIotaExpressionLambdaExpressionNegatedExpression OrExpressionVariable is_indvarc]tRt^,tRtR#)ErrorN__name__ __module__ __qualname____firstlineno____static_attributes__r3/usr/lib/python3/dist-packages/nltk/sem/evaluate.pyrr,rrc]tRt^0tRtR#) UndefinedrNrrrrr"r"0r rr"c \P!V4p\\V^,V44pVP RR4'd4\ 4VP 4Fp\ RV,4K V!V/VB#)traceNz%s => %s)inspectgetfullargspecdictzippopprintitems)fargskwargspecditems&*, rr%r%4sh$$Q'G ST "#AuuWd GGID *t# $ d>b>rc\V4^8XdR#\;QJdRV4F 'dK RM RM !RV44'd.\\V44\\V448XdR#\ RV,4h)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 Tc3B"TFp\V\4xK R#5iN) isinstancetuple).0els& r is_rel..Js /QrZE " "QsFz.Set %r contains sequences of different lengths)lenallmaxmin ValueError)ss&ris_relrB>s^ 1v{  /Q / /Q / / /CAK3s1v;4NIAMNNrc\4pVFpp\V\4'dVPV34K-\V\4'dVP\V44K_VPV4Kr V#)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 )setr6straddint)rAnewelems& rset2relrJPs_ %C dC GGTG  c " " GGCI  GGDM  Jrc\\V4^8Xd^#\\V4^,4#)zU Check the arity of a relation. :type rel: set of tuples :rtype: int of tuple of str )r<list)rels&rarityrNhs%  3x1} tCy| rcraa]tRt^stoRtV3RltRtRt]R4t ]R4t ] R4t Rt VtV;t#) Valuationa 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 :<\SV`4VFwr#\V\4'g\V\4'dW0V&K7\V\ 4'd\ V4W&K\\P!RV: RV: 2^BR7p\V4h R#)z- :param xs: a list of (symbol, value) pairs. z@Error in initializing Valuation. Unrecognized value for symbol 'z': )widthN) super__init__r6rEboolrDrJtextwrapfillr@)selfxssymvalmsg __class__s&& rrTValuation.__init__s| HC#s##z#t'<'<S C%%#CL mmADcK !o%rc\W9d\PW4#\RV,4h)zUnknown expression: '%s'r( __getitem__r"rXkeys&&rraValuation.__getitem__s) ;##D. .6<= =rc\V4#r5rrXs&r__str__Valuation.__str__s t}rc  8.pVP4Ftp\V\4'dVPV4K,\V\4'dKDTP VUUu.uFq3F qDfKVNK K upp4Kv \ V4#uuppi)z7Set-theoretic domain of the value-space of a Valuation.)valuesr6rEappendrUextendrD)rXdomr[tuple_rIs& rdomainValuation.domainsw;;=C#s## 3T** (+SfTTTS !3xTs ' B 5 B c 4\VP44#)z9The non-logical constants which the Valuation recognizes.)sortedkeysrfs&rsymbolsValuation.symbolssdiik""rc\V4#r5)read_valuation)clsrAs&&r fromstringValuation.fromstrings a  rr)rrrr__doc__rTrargpropertyrort classmethodryr__classdictcell__ __classcell__r] __classdict__s@@rrPrPssZ &&>   ##!!!rrPz \s*=+>\s*z\s*,\s*zg\s* (\([^)]+\)) # tuple-expression \s*c\PV4pV^,pV^,pVPR4'dV^Rp\P V4pV'dA.pVF7pV^Rp\ \ PV44pVPV4K9 M\ PV4p\V4pW#3#)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 {) _VAL_SPLIT_REsplit startswith _TUPLES_REfindallr7_ELEMENT_SPLIT_RErkrD)rApiecessymbolvalue tuple_strings set_elementstselements& r_read_valuation_liners  #F AYF 1IE a "**51 L#"X 1 7 7 ;<##G,$ -2259LL! =rcjVeVPV4p.p\VP44FPwr4VP4pVP R4'gVR8XdK5VP \ V44KR \V4# \dp\RT RT 24ThRp?ii;i)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 splitlinesstriprrkrr@rP)rAencoding statementslinenumlinees&& rrwrws HHX J"1<<>2 zz| ??3  42:  O   248 9 3 Z   O4WIRvFGQ N Os'B B2B--B2cbaa]tRt^toRtR V3RlltRtRtR RltRt Rt Rt R t Vt V;t#) 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,<\SV`4WnV'd`VFYwr4W@P9g"QRPVVP44h\ V4'gQRV,4hW@V&K[ RVnVP 4R#)z'{}' is not in the domain: {}-Wrong format for an Individual Variable: '%s'N)rSrTroformatrvariant _addvariant)rXroassignvarr[r]s&&& rrTAssignment.__init__0s  "kk)+J+Q+QKK,)!~~CcI~ S #  rc\W9d\PW4#\RV,4h)z"Not recognized as a variable: '%s'r`rbs&&rraAssignment.__getitem__@s) ;##D. .@3FG GrcR\VP4pVPV4V#r5)rroupdate)rXrHs& rcopyAssignment.copyFs!% 4 rc \V'dWMVP4VP4R#)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)rXrs&&rpurgeAssignment.purgeKs$  JJL rc jRp\VP4pVFwr4VRV RV R2, pK V#)zA Pretty printing for assignments. {'x', 'u'} appears as 'g[u/x]' g[/])rrr)rXgstringrr[rs& rrgAssignment.__str__YsA&HC 3%qQ' 'G rc .pVP4F&pV^,V^,3pVPV4K( WnR#)z; Create a more pretty-printable version of the assignment. N)r,rkr)rXlist_r2pairs& rrAssignment._addvariantdsAJJLDGT!W%D LL ! rc W P9gQV RVP 24h\V4'gQRV,4hW V&VP4V#)zP Add a new variable-value pair to the assignment, and update ``self.variant``. z is not in the domain r)rorr)rXrr[s&&&rrFAssignment.addos[ kk!NcU*@ #NN!~~TNQTTT~S   r)rorr5)rrrrr{rTrarrrgrrFrr~rrs@@rrrs42h H      rrc^a]tRtRtoRtRtRtRtR RltR Rlt R R lt RR lt R t Vt R#)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\V\4'gQhWnW nVP VP4'g\ RVP: RV: 24hR#)zThe valuation domain, z*, must be a subset of the model's domain, N)r6rDro valuation issupersetr)rXrors&&&rrTModel.__init__sX&#&&&& "  !1!122##V- 3rc@RVP: RVP: R2#)(z, )rorrfs&r__repr__Model.__repr__s 4;;/DNN#5Q77rc:RVP RVP 2#)z Domain = z, Valuation = rrfs&rrg Model.__str__s4;;-'88HIIrNc \P!V4pVPWBVR7pV'd\4\RV RV RV 24V# \d(T'd\4\RT RT 24R#i;i)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 rysatisfyr+r")rXexprrr%parsedrs&&&& revaluateModel.evaluates **40FLL%L8E$ugZsCDL $7s;<  sAAB&BBc | aa\V\4'dVP4wrE\V\4'dKSP VS4p\ ;QJd.VV3RlV4FNK 5M!VV3RlV44pWv9#SP VP S4pSP VPS4pWh,#\V\4'd"SP VPS4'*#\V\4'dASP VPS4;'dSP VPS4#\V\4'dASP VPS4;'gSP VPS4#\V\4'dFSP VPS4'*;'gSP VPS4#\V\4'd:SP VPS4SP VPS48H#\V\ 4'd:SP VPS4SP VPS48H#\V\"4'dqSP%4p SP&FNp V P)VP*P,V 4SP VPV 4'dKMR# R#\V\.4'dqSP%4p SP&FNp V P)VP*P,V 4SP VPV 4'gKMR# R#\V\04'dqSP%4p SP&FNp V P)VP*P,V 4SP VPV 4'gKMR# R#\V\24'd]/p VP*P,p SP&F2p SP VPSP)W44p WV &K4 V #SP5VSV4#)a Recursive interpretation function for a formula of first-order logic. Raises an ``Undefined`` error when ``parsed`` is an atomic string but is not a symbol or an individual variable. :return: Returns a truth value or ``Undefined`` if ``parsed`` is complex, and calls the interpretation function ``i`` if ``parsed`` is atomic. :param parsed: An expression of ``logic``. :type g: Assignment :param g: an assignment to individual variables. c3H<"TFpSPVS4xK R#5ir5)r)r8argrrXs& rr: Model.satisfy..sJ  S! 4 4 s"FT)r6runcurryrrr7functionargumentrtermrfirstsecondrr r r rrrorFvariablenamer rri)rXrrr%r argumentsfunvalargvalsargvalnew_gucfrr[sf&f& rr Model.satisfys` f3 4 4"(.."2 H($>??h2%J J%%J JJ((fooq9fooq9~%  1 2 2||FKK33 3  . .<< a0SST\\&--QR5S S  - -<< a0RRDLLPQ4R R  . . V\\155XX$,,v}}VW:X X  . .<< a0DLLPQ4RR R  2 3 3<< a0DLLPQ4RR R  . .FFHE[[ &//..2||FKK77 !  0 1 1FFHE[[ &//..2<< U33!  / /FFHE[[ &//..2<< U33!  0 1 1B//&&C[[ll6;;c > 1 !I66&!U+ +rc 6VPPVPP9d(VPVPP,#\ V\ 4'dW!PP,#\ RV,4h)ax An interpretation function. Assuming that ``parsed`` is atomic: - if ``parsed`` is a non-logical constant, calls the valuation *V* - else if ``parsed`` is an individual variable, calls assignment *g* - else returns ``Undefined``. :param parsed: an ``Expression`` of ``logic``. :type g: Assignment :param g: an assignment to individual variables. :return: a semantic value zCan't find a value for %s)rrrrtr6rr")rXrrr%s&&&&rrModel.ism$ ??  4>>#9#9 9>>&//"6"67 7  < = =__))* *7&@A Arc  :RpWfV,,p.p\V\4'd \V4p MTp WP49Ed2V'd)\ 4\ We,RV RV 2,4VP Fp VP 4p V PV PV 4V'dV^8d V^, p M^p VPWV 4p V'd\ VRV ,,4V R8Xd&V'd\ VRV RV R2,4KKVPV 4V'gK\ VRV RV R V 2,4K VUu0uFqkK ppV#\V P R V 24huupi) 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 z(trying assignment %s)Fz value of 'z' under z is Falsez is z is not free in ) r6rErfreer+rorrFrrrkr")rXrvarexrr%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-s0 Frr5)F)Nr$)rrrrr{rTrrgrrrrrr~)rs@rrr|s6"8J,I,XB499rrc <\.RO4s\4s\ \\4s\ \4s\4\R\,4\R4\R\,4\R4\4\R\ 4\R\,4.R OpVF[pV'd(\4\ PV\V4K2\RV R\ PV\4 24K] R#) z!Example of a propositional model.*zPropositional Formulas Demoz7(Propositional constants treated as nullary predicates)z Model m1: The value of '' is: N))PT)QT)RF)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)) rPval1rDdom1rm1rg1r+multr)r% sentencessents& rpropdemor_s = >D 5D tT B D B G #* '( #* CD G - #*I(  G KKb% ( N4&r{{4/D.EF G rc RRRRRR03RRR03RR03R 0Rm3.s\\4s\Ps\ \\4s\\RR.4sV'EgM\4\R \,4\R 4\R \,4\R RR \ 4\R\4.ROpVUu.uFp\P!V4NK pp\4VF/p\RV: R\ PV\4: 24K1 .ROpVFuwrx\ P\P!V4\4p \;QJd.RV4FNK 5M !RV44p \V RV RW9 24Kw R#R#uupi \d\RT,4Ki;i \d\T RT R24Ki;i) zExample of a first-order model.b1rd1girlg2boyb2dogloverz Models Demoz Model m2:  zVariable assignment = zThe interpretation of 'z ' in m2 is z-The interpretation of '%s' in m2 is Undefinedc3~"TF3p\P\P!V4\4xK5 R#5ir5)m2rr ryr )r8rs& rr:folmodel..s+UPTZ%:%:3%? D DPTs;=rz) evaluates to z) evaluates to UndefinedN)adamr )bettyr)fidor >r rrr rr r r )xr )yr z--------------)rr rwalksrrz))r r)r)r)r)rr)r)rr)v2rPval2rodom2rrrr r+rr ryrr"r7) quietr%exprsr parsed_exprsr applicationsfunr.rargsvals && rfolmodelr)s  $ t   IJ B R=D ;;D tT B D; 4 5B 5  cDj m cDj mXtR0 &+?:?@%Q --a0% @ "F PrttFB/1# &IC ?j33C8"=%UPTU%%UPTUUQtfOG4E3FGH &9 A PENO P ?Qtf$<=> ?s+F5+F:>A/G:GGG>=G>c ~\RR7\4\R\,4\R4\R\,4.ROpVFep\P 4V'd\ P V\V4K<\RV R\ P V\4 24Kg R#) z> Interpretation of closed expressions in a first-order model. Tr#rzFOL Formulas DemorrN)zlove (adam, betty)z (adam = mia)z\x. (boy(x) | girl(x))z\x. boy(x)(adam)z\x y. love(x, y)z\x y. love(x, y)(adam)(betty)z\x y. love(x, y)(adam, betty)z\x y. (boy(x) & love(x, y))z#\x. exists y. (boy(x) & love(x, y))zexists z1. boy(z1)z!exists x. (boy(x) & -(x = adam))z&exists x. (boy(x) & all y. love(y, x))zall x. (boy(x) | girl(x))z1all x. (girl(x) -> exists y. boy(y) & love(x, y))z3exists x. (boy(x) & all y. (girl(y) -> love(y, x)))z3exists x. (boy(x) & all y. (girl(y) -> love(x, y)))zall x. (dog(x) -> - girl(x))z-exists x. exists y. (love(x, y) & love(x, y)))r)r+rr rrr)r%formulasfmlas& rfoldemor.s 4 G #*  #*H*   KKb% ( N4&r{{4/D.EF G rc "\4\R\,4\R4\R\,4\RR7.ROpV'd\\4VF$p\V4\P !V4K& VUu.uFp\P !V4NK ppVFLp\ P4\RPV\PVR\ V444KN R#uupi) z5Satisfiers of an open formula in a first order model.rzSatisfiers DemoTr+zThe satisfiers of '{}' are: {}rN)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))r0z&exists y. (love(adam, y) & love(y, x))) r+rr)rr ryr rrr)r%r,r-rps& rsatdemor2s G #*  #* 4H,  b  d d#7? ?hdj##D)hF ?    , 3 3Ar}}QRQV7W X @sD c^\^\^\^\/pW ,!VR7R# \dTFpY ,!TR7K R#i;i)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 rN)rr)r.r2KeyError)numr%demoss&& rdemor7(sL!Xq'1g >E$  $C JU #$s-#AA__main__rr5)FN)r$N)3r{r&resysrVpprintrnltk.decoratorsrnltk.sem.logicrrrrr r r r r rrrrrrr Exceptionrr"r%rBrJrNr(rPcompilerrVERBOSErrrwrrrrr)r.r2r7rrrrrAs  %( I   O$0<!<!D <( JJz* ZZ'JJ   F!2~~BWW|  *Hb5?x%HX- `$* z!r