U ef@svdZddlZddlZddlZddlZddlmZddlmZddl m Z m Z m Z m Z mZmZmZmZmZmZmZmZmZmZmZmZGdddeZGdd d eZd d Zd d ZddZddZ Gddde!Z"e#dZ$e#dZ%e#dej&Z'ddZ(d.ddZ)Gddde!Z*GdddZ+dZ,d/d d!Z-d0d#d$Z.d1d%d&Z/d2d'd(Z0d3d)d*Z1e2d+krre1d,dd-dS)4zK This module provides data structures for representing first-order models. Npformat) decorator)AbstractVariableExpression AllExpression AndExpressionApplicationExpressionEqualityExpressionExistsExpression Expression IffExpression ImpExpressionIndividualVariableExpressionIotaExpressionLambdaExpressionNegatedExpression OrExpressionVariable is_indvarc@s eZdZdS)ErrorN__name__ __module__ __qualname__rrR/var/www/html/assets/scripts/venv/lib/python3.8/site-packages/nltk/sem/evaluate.pyr,src@s eZdZdS) UndefinedNrrrrrr0srcOsRt|}tt|d|}|ddrHt|D]}td|q6|||S)Nrtracez%s => %s)inspectgetfullargspecdictzippopprintitems)fargskwZargspecditemrrrr4s   rcCsNt|dkrdStdd|Dr>tt|tt|kr>dStd|dS)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 rTcss|]}t|tVqdSN) isinstancetuple).0elrrr Jszis_rel..z.Set %r contains sequences of different lengthsN)lenallmaxmin ValueError)srrris_rel>s *r6cCsPt}|D]@}t|tr&||fq t|tr@|t|q ||q |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 )setr+straddint)r5newelemrrrset2relPs    r=cCs t|dkrdStt|dS)ze Check the arity of a relation. :type rel: set of tuples :rtype: int of tuple of str r)r0list)relrrrarityhs r@csTeZdZdZfddZddZddZedd Zed d Z e d d Z Z 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. cspt|D]\\}}t|ts*t|tr4|||<qt|trLt|||<qtjd||fdd}t |qdS)z= :param xs: a list of (symbol, value) pairs. zGError in initializing Valuation. Unrecognized value for symbol '%s': %sB)widthN) super__init__r+r8boolr7r=textwrapfillr4)selfZxssymvalmsg __class__rrrEs    zValuation.__init__cCs$||krt||Std|dS)NzUnknown expression: '%s'r __getitem__rrIkeyrrrrPs zValuation.__getitem__cCst|Sr*rrIrrr__str__szValuation.__str__cCsNg}|D]8}t|tr&||q t|ts |dd|Dq t|S)z7Set-theoretic domain of the value-space of a Valuation.cSs"g|]}|D]}|dk r |q qSr*r)r-tuple_r<rrr s z$Valuation.domain..)valuesr+r8appendrFextendr7)rIdomrKrrrdomains     zValuation.domaincCs t|S)z9The non-logical constants which the Valuation recognizes.)sortedkeysrSrrrsymbolsszValuation.symbolscCst|Sr*)read_valuation)clsr5rrr fromstringszValuation.fromstring) rrr__doc__rErPrTpropertyr[r^ classmethodra __classcell__rrrMrrAss   rAz \s*=+>\s*z\s*,\s*zg\s* (\([^)]+\)) # tuple-expression \s*cCst|}|d}|d}|dr|dd}t|}|rrg}|D](}|dd}tt|}||qFn t|}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_REfindallr,_ELEMENT_SPLIT_RErXr7)r5piecessymbolvalueZ tuple_stringsZ set_elementstselementrrr_read_valuation_lines      rtc Cs|dk r||}g}t|D]p\}}|}|ds"|dkrFq"z|t|Wq"tk r}ztd|d||W5d}~XYq"Xq"t|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 splitlinesstriprkrXrtr4rA)r5encodingZ statementsZlinenumlineerrrr_s  *r_csTeZdZdZdfdd ZddZddZdd d Zd d Zd dZ ddZ Z 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 Ncslt||_|rZ|D]@\}}||jks.FTN)r+rZuncurryrrr,functionargumentrtermrfirstsecondrr r r rrr[r9variablenamer rri)rIrrrr argumentsfunvalZargvalsargvalnew_gucfrrKrrrrsd                        z Model.satisfyFcCsD|jj|jjkr|j|jjSt|tr4||jjStd|dS)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 %sN)rrrr^r+rr)rIrrrrrrrs   zModel.irc Cs:d}|||}g}t|tr(t|} n|} | |kr"|r`tt||d|d||jD]} |} | | j| |r|dkr|d} nd} | || | } |rt|d| | dkr|rt|d|d | d qf| | |rft|d|d | d | qfd d |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 rfrz(trying assignment %s)Fz value of 'z' under z is Falsez is cSsh|]}|qSrr)r-crrr Nsz#Model.satisfiers..z is not free in ) r+r8rfreer#r[rr9rrrXr)rIrZvarexrrZnestingZspacerindent candidatesrrrZlowtracerqresultrrr satisfierss@         zModel.satisfiers)N)N)F)Nr) rrrrbrErrTrrrrrrrrr|s   L rcCstdddgatatttattattdt tdtdt tdttdttdt dd d d d d dddddddddddg}|D]:}|rtt |t|qtd|dt |tqdS)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) rAZval1r7Zdom1rm1r~g1r#multr)rZ sentencessentrrrpropdemo^sF     rFc Csddddddhfddd hfd d hfd d dddhfgattatjatttattddga|st t dt t dt dt t dddtt dtddd ddddg}dd|D}t |D]D}zt d |t |tfWqt k r t d!|YqXqd"d#d$d%g}|D]z\}}zDt t |t}td&d'|D} t |d(|d)| |kWn*t k rt |d(|d*YnXqd+S),zExample of a first-order model.)adamb1)Zbettyr)Zfidod1girlrg2boyrb2dogrlove)rr)rr)rr)rr)xr)yrrz Models Demoz Model m2: z-------------- zVariable assignment = rwalksrrzcSsg|]}t|qSrr ra)r-r}rrrrVszfolmodel..z&The interpretation of '%s' in m2 is %sz-The interpretation of '%s' in m2 is Undefined)rr)r)r)r)rr)r)rrcss |]}tt|tVqdSr*)m2rr rarrrrrr/szfolmodel..rz) evaluates to z) evaluates to UndefinedN)Zv2rAZval2r[Zdom2rrr~rr#rrrr rar,) quietrexprsZ parsed_exprsrZ applicationsZfunr&rZargsvalrrrfolmodelsV         rcCstddttdttdtdtddddd d d d d dddddddddg}|D]<}t|r|t|t|q\td|dt|tq\dS)zF Interpretation of closed expressions in a first-order model. TrrzFOL Formulas Demozlove (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#rrrrr)rformulasfmlarrrfoldemos:   rcCsttdttdtdttddddddd d d d d ddddddddd dg}|rftt|D]}t|t|qjdd|D}|D](}ttd|t |dt|qdS)z5Satisfiers of an open formula in a first order model.rzSatisfiers DemoTrzboy(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)zexists 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))z&exists y. (love(adam, y) & love(y, x))cSsg|]}t|qSrr)r-rrrrrVszsatdemo..zThe satisfiers of '{}' are: {}rN) r#rrrr rarrrr)rrrrprrrsatdemosH    rcCsRttttd}z|||dWn,tk rL|D]}|||dq4YnXdS)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 )rfrN)rrrrKeyError)numrZdemosrrrdemo's r__main__rr)N)N)FN)N)N)rN)3rbrresysrGpprintrZnltk.decoratorsrZnltk.sem.logicrrrrr r r r r rrrrrrr Exceptionrrrr6r=r@r rAcompilerirnVERBOSErlrtr_r~rrrrrrrrrrrr sD  H  B  # _ 1 < , 0