'[ffdZddlZddlZddlZddlZddlmZddlmZddl m Z m Z m Z m Z mZmZmZmZmZmZmZmZmZmZmZmZGddeZGdd eZd Zd Zd Zd Z Gdde!Z"ej#dZ$ej#dZ%ej#dej&Z'dZ(d#dZ)Gdde!Z*GddZ+dZ,d#dZ-d$dZ.d#dZ/d#dZ0d%dZ1e2d kre1d!d"dSdS)&zK This module provides data structures for representing first-order models. Npformat) decorator)AbstractVariableExpression AllExpression AndExpressionApplicationExpressionEqualityExpressionExistsExpression Expression IffExpression ImpExpressionIndividualVariableExpressionIotaExpressionLambdaExpressionNegatedExpression OrExpressionVariable is_indvarceZdZdS)ErrorN__name__ __module__ __qualname__E/var/www/piapp/venv/lib/python3.11/site-packages/nltk/sem/evaluate.pyrr,DrrceZdZdS) UndefinedNrrrrr!r!0rrr!ctj|}tt|d|}|ddr7t |D]}t d|z||i|S)Nrtracez%s => %s)inspectgetfullargspecdictzippopprintitems)fargskwargspecditems rr#r#4s$Q''G ST " "##AuuWd% GGII % %D *t# $ $ $ $ 1d>b>>rct|dkrdStd|Drzis_rel..Js, / /rZE " " / / / / / /rz.Set %r contains sequences of different lengths)lenallmaxmin ValueError)ss ris_relr?>ss 1vv{{t / /Q / / / / /OCAKK3s1vv;;4N4NtIAMNNNrct}|D]{}t|tr||f.t|tr#|t|f||||S)aR 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 )setr4straddint)r>newelems rset2relrGPs %%C dC   GGTG     c " "  GGCII     GGDMMMM Jrcpt|dkrdStt|dS)ze Check the arity of a relation. :type rel: set of tuples :rtype: int of tuple of str r)r9list)rels rarityrKhs0  3xx1}}q tCyy|  rcpeZdZdZfdZdZdZedZedZ e dZ xZ S) 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\t|D]\}}t|tst|tr|||<5t|t rt |||<]tjd|d|d}t|dS)z= :param xs: a list of (symbol, value) pairs. z@Error in initializing Valuation. Unrecognized value for symbol 'z': B)widthN) super__init__r4rBboolrArGtextwrapfillr=)selfxssymvalmsg __class__s rrRzValuation.__init__s  & &JS##s## &z#t'<'< &S C%% &#CLLS mmADccK !oo% & &rcd||vrt||Std|z)NzUnknown expression: '%s'r& __getitem__r!rVkeys rr^zValuation.__getitem__s5 $;;##D#.. .6<== =rc t|Sr3rrVs r__str__zValuation.__str__st}}rcg}|D]a}t|tr||-t|ts|d|Dbt |S)z7Set-theoretic domain of the value-space of a Valuation.c g|] }|D]}|| Sr3r)r6tuple_rFs r z$Valuation.domain..s*SSSfSS$BRTBRBRBRBRr)valuesr4rBappendrSextendrA)rVdomrYs rdomainzValuation.domains;;==  C#s##  3T**  SSSSS3xxrcDt|S)z9The non-logical constants which the Valuation recognizes.)sortedkeysrbs rsymbolszValuation.symbolssdiikk"""rc t|Sr3)read_valuation)clsr>s r fromstringzValuation.fromstringsa   r) rrr__doc__rRr^rcpropertyrlrp classmethodrt __classcell__r[s@rrMrMss  &&&&&&>>>   X ##X#!![!!!!!rrMz \s*=+>\s*z\s*,\s*zg\s* (\([^)]+\)) # tuple-expression \s*ct|}|d}|d}|dr|dd}t|}|rNg}|D]H}|dd}t t |}||Int |}t|}||fS)a 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_REfindallr5_ELEMENT_SPLIT_RErirA)r>piecessymbolvalue tuple_strings set_elementstselements r_read_valuation_liners  # #F AYF 1IE  "ad "**511  :L# - -"X 1 7 7 ; ;<<##G,,,, - -22599LL!! 5=rc|||}g}t|D]\}}|}|ds|dkr5 |t |Y#t$r}td|d||d}~wwxYwt|S)a 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 splitlinesstriprrirr=rM)r>encoding statementslinenumlinees rrrrrs HHX  J"1<<>>22OO zz|| ??3   42::  O   2488 9 9 9 9 O O OFWFFFFGGQ N O Z  s1"B B9B44B9cJeZdZdZd fd ZdZdZd dZdZdZ d Z xZ S) Assignmentae 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 Nc:t||_|rU|D]R\}}||jvs#Jd||jt |s Jd|z|||<Sd|_|dS)Nz'{}' is not in the domain: {}-Wrong format for an Individual Variable: '%s')rQrRrlformatrvariant _addvariant)rVrlassignvarrYr[s rrRzAssignment.__init__0s   $  cdk)))+J+Q+QK,,)))!~~CcI S   rcd||vrt||Std|z)Nz"Not recognized as a variable: '%s'r]r_s rr^zAssignment.__getitem__@s5 $;;##D#.. .@3FGG GrcXt|j}|||Sr3)rrlupdate)rVrEs rcopyzAssignment.copyFs(%% 4 rcb|r||=n||dS)z Remove one or all keys (i.e. logic variables) from an assignment, and update ``self.variant``. :param var: a Variable acting as a key for the assignment. N)clearr)rVrs rpurgezAssignment.purgeKs9  S JJLLL trcZd}t|j}|D]\}}|d|d|dz }|S)zQ Pretty printing for assignments. {'x', 'u'} appears as 'g[u/x]' g[/])rnr)rVgstringrrYrs rrczAssignment.__str__YsP&&! ( (JS# '3''''' 'GGrcg}|D]'}|d|df}||(||_dS)zK Create a more pretty-printable version of the assignment. r{rN)r*rir)rVlist_r0pairs rrzAssignment._addvariantdsSJJLL  DGT!W%D LL     trc||jvsJ|d|jt|s Jd|z|||<||S)zh Add a new variable-value pair to the assignment, and update ``self.variant``. z is not in the domain r)rlrr)rVrrYs rrCzAssignment.addosp dk!!!c#N#N#N#N!!!~~TTNQTTTTTS   rr3) rrrrurRr^rrrcrrCrxrys@rrrs22h HHH                  rrcDeZdZdZdZdZdZd dZd dZd d Z dd Z dS)Modela[ A first order model is a domain *D* of discourse and a valuation *V*. A domain *D* is a set, and a valuation *V* is a map that associates expressions with values in the model. The domain of *V* should be a subset of *D*. Construct a new ``Model``. :type domain: set :param domain: A set of entities representing the domain of discourse of the model. :type valuation: Valuation :param valuation: the valuation of the model. :param prop: If this is set, then we are building a propositional model and don't require the domain of *V* to be subset of *D*. ct|tsJ||_||_||jst d|jd|dS)NzThe valuation domain, z*, must be a subset of the model's domain, )r4rArl valuation issupersetr)rVrlrs rrRzModel.__init__sr&#&&&&& "  !122 %###VV-   rc(d|jd|jdS)N(z, )rlrrbs r__repr__zModel.__repr__s74;77DN7777rc&d|jd|jS)Nz Domain = z, Valuation = rrbs rrcz Model.__str__sI4;IIIIIrNc tj|}||||}|r&ttd|d|d||S#t$r)|r#ttd|d|YdSwxYw)aA 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 rtsatisfyr)r!)rVexprrr#parsedrs revaluatezModel.evaluates *400FLL%L88E EC$CCuCCCCDDDL    =;$;;;;<<<;;  sAA/B  B cpt|tr|\}}t|tr6|}t fd|D}||vS|j}|j}||St|tr|j  St|tr6|j o|j St|tr6|j p|j St|tr7|j  p|j St|tr8|j |j kSt|t r8|j |j kSt|t"r^} jD]@} | |jj| |j | sdSAdSt|t.r^} jD]@} | |jj| |j | rdSAdSt|t0r^} jD]@} | |jj| |j | rdSAdSt|t2rNi} |jj} jD]6} |j | | } | | | <7| S||S)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. c3DK|]}|VdSr3)r)r6argrrVs rr8z Model.satisfy..s1JJ S! 4 4JJJJJJrFT)r4r uncurryrrr5functionargumentrtermrfirstsecondrrr r rrrlrCvariablenamer rri)rVrrr#r argumentsfunvalargvalsargvalnew_gucfrrYs` ` rrz Model.satisfys f3 4 49 ,"(.."2"2 Hi($>?? &h22JJJJJ JJJJJ&((foq99foq99f~%  1 2 2- ,||FK333 3  . .+ ,<< a00ST\\&-QR5S5S S  - -) ,<< a00RDLLPQ4R4R R  . .' , V\1555X$,,v}VW:X:X X  . .% ,<< a00DLLPQ4R4RR R  2 3 3# ,<< a00DLLPQ4R4RR R  . .! ,FFHHE[ ! ! &/.222||FK77! 55!4  0 1 1 ,FFHHE[   &/.222<< U33 44 5  / / ,FFHHE[   &/.222<< U33 44 5  0 1 1 ,B/&C[  ll6;c1 >> 1I66&!U++ +rFc|jj|jjvr|j|jjSt |t r||jjSt d|z)a 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)rrrrpr4rr!)rVrrr#s rrzModel.ise$ ? 4>#9 9 9>&/"67 7  < = = BV_)* *7&@AA Arrc d}|||zz}g}t|trt|} n|} | |vr|r)t t ||zd|d|z|jD]} |} | | j| |r |dkr|dz } nd} | || | } |rt |d| zz| dkr|rt |d|d | d z| | |rt |d|d | d | zd |D}nt| jd ||S)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 r{rz(trying assignment %s)Fz value of 'z' under z is Falsez is ch|]}|Srr)r6cs r z#Model.satisfiers..Ns,,,Aa,,,rz is not free in ) r4rBrfreer)rlrrCrrrir!)rVrvarexrr#nestingspacerindent candidatesrrrlowtracerresults r satisfierszModel.satisfierss6G+, eS ! ! 5//CCC &++--   g%G&GGAGGH[ X X #(A&&&!UQYY$qyHH H VUH==E&#;e#CCDDDE>>Vf'TF'T'TE'T'T'TTUUU%%a(((Xf'VF'V'VE'V'Vu'V'VVWWW,,,,,FFsxAAAABB B rr3)F)Nr) rrrrurRrrcrrrrrrrrr|s"888JJJ,I,I,I,I,XBBBB4999999rrc tgdatat ttat tattdtztdtdtztdttdt tdtzgd}|D]g}|r0tt |t|4td|dt |thd S) z!Example of a propositional model.))PT)QT)RF*zPropositional Formulas Demoz7(Propositional constants treated as nullary predicates)z Model m1: )z(P & Q)z(P & R)z- Pz- Rz- - Pz - (P & R)z(P | R)z(R | P)z(R | R)z (- P | R)z (P | - P)z(P -> Q)z(P -> R)z(R -> P)z (P <-> P)z (R <-> R)z (P <-> R)The value of '' is: N) rMval1rAdom1rm1rg1r)multr)r# sentencessents rpropdemor^s> === > >D 55D tT  B D  B GGG #* '((( #* CDDD GGG - #*I(HH  H GGG KKb% ( ( ( ( F4FFr{{4/D/DFF G G G G HHrFc ddddddhfddd hfd d hfd hd fgattatjat ttattddga|sttdtztdtdtztdddt tdtgd}d|D}t|D]X} td|dt |t7#t$rtd|zYUwxYwgd}|D]\}} t tj|t}td|D} t|d|d| |vk#t$rt|d|dYwxYwd Sd S)!zExample of a first-order model.)adamb1)bettyr)fidod1girlrg2boyrb2dogrlove>rrrrrrrr)xr)yrrz Models Demoz Model m2: z-------------- zVariable assignment = )rrrwalksrrzc6g|]}tj|Srr rt)r6rs rrgzfolmodel..s#@@@Q -a00@@@rzThe interpretation of 'z ' in m2 is z-The interpretation of '%s' in m2 is Undefined))rr)r)r)r)rr)r)rrc3zK|]6}ttj|tV7dSr3)m2rr rtr)r6rs rr8zfolmodel..s;UUZ%:3%?%? D DUUUUUUrrz) evaluates to z) evaluates to UndefinedN)v2rMval2rldom2rr rrr)rrr!r rtr5) quietr#exprs parsed_exprsr applicationsfunr,rargsvals rfolmodelrs{  $ t   IIIJ B R==D ;D tT  B D; 4 5 5B "?  cDj m cDj mXtR000 &+++???@@%@@@  " P PF PvvrttFB///1 P P PENOOOOO P   ( ? ?KS$ ?j3C88"==UUPTUUUUUGGtGGGv4EGGHHHH ? ? ?==t===>>>>> ?C"?"?8 ? ?s%3D;;EE)A$GG0/G0c tdttdtztdtdtzgd}|D]r}t|r"t |t|?td|dt |tsdS) zF Interpretation of closed expressions in a first-order model. TrrzFOL 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)rr)rrrr r)r#formulasfmlas rfoldemors 4 GGG #*  #*H*HH   H KKb% ( ( ( ( F4FFr{{4/D/DFF G G G G HHrc ttdtztdtdtztdgd}|rtt|D]%}t|t j|&d|D}|D]^}t td|t |dt |_d S) z5Satisfiers of an open formula in a first order model.rzSatisfiers DemoTr)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))rz&exists y. (love(adam, y) & love(y, x))c6g|]}tj|Srr )r6rs rrgzsatdemo..s# ? ? ?dj#D)) ? ? ?rzThe satisfiers of '{}' are: {}rN) r)rrr r rtrrrr)r#rrrps rsatdemor!s GGG #*  #* 4H,  b $$ d d#### ? ?h ? ? ?F      , 3 3Ar}}QRQV7W7W X X      rcttttd} |||dS#t$r|D]}|||YdSwxYw)aO Run exists demos. - num = 1: propositional logic demo - num = 2: first order model demo (only if trace is set) - num = 3: first order sentences demo - num = 4: satisfaction of open formulas demo - any other value: run all the demos :param trace: trace = 1, or trace = 2 for more verbose tracing )r{rN)rrrr!KeyError)numr#demoss rdemor)'sX'g > >E$c  $$$ $ $C E#JU # # # # # $ $ $$s1!AA__main__r#rr3)FN)rN)3rur$resysrTpprintrnltk.decoratorsrnltk.sem.logicrrrr r r r r rrrrrrrr Exceptionrr!r#r?rGrKr&rMcompiler~rVERBOSErrrrrrrrrrr!r)rrrrr3s>  %%%%%%(     I           OOO$0<!<!<!<!<!<!<!<!D <(( BJz** RZ'J     F!!!!2~~~~~~~~BWWWWWWWW| *H*H*H*Hb5?5?5?5?x%H%H%H%HX- - - - `$$$$* zD!r