o rZhfc@sxdZddlZddlZddlZddlZddlmZddlmZddl m Z m Z m Z m Z mZmZmZmZmZmZmZmZmZmZmZmZGdddeZGdd d eZd d Zd d ZddZddZ Gddde!Z"e#dZ$e#dZ%e#dej&Z'ddZ(d.ddZ)Gddde!Z*GdddZ+dZ,d.d d!Z-d/d#d$Z.d.d%d&Z/d.d'd(Z0d0d)d*Z1e2d+kre1d,dd-dSdS)1zK This module provides data structures for representing first-order models. Npformat) decorator)AbstractVariableExpression AllExpression AndExpressionApplicationExpressionEqualityExpressionExistsExpression Expression IffExpression ImpExpressionIndividualVariableExpressionIotaExpressionLambdaExpressionNegatedExpression OrExpressionVariable is_indvarc@ eZdZdS)ErrorN__name__ __module__ __qualname__rr@/var/www/auris/lib/python3.10/site-packages/nltk/sem/evaluate.pyr,rc@r) UndefinedNrrrrrr0rrcOsVt|}tt|d|}|ddr$t|D]}td|q||i|S)Nrtracez%s => %s)inspectgetfullargspecdictzippopprintitems)fargskwZargspecditemrrrr4s   rcCsJt|dkrdStdd|Drtt|tt|krdStd|)z Check whether a set represents a relation (of any arity). :param s: a set containing tuples of str elements :type s: set :rtype: bool rTcss|]}t|tVqdSN) isinstancetuple).0elrrr Jszis_rel..z.Set %r contains sequences of different lengths)lenallmaxmin ValueError)srrris_rel>s * r8cCsPt}|D] }t|tr||fqt|tr |t|q||q|S)aR Convert a set containing individuals (strings or numbers) into a set of unary tuples. Any tuples of strings already in the set are passed through unchanged. For example: - set(['a', 'b']) => set([('a',), ('b',)]) - set([3, 27]) => set([('3',), ('27',)]) :type s: set :rtype: set of tuple of str )setr-straddint)r7newelemrrrset2relPs    r?cCs t|dkrdStt|dS)ze Check the arity of a relation. :type rel: set of tuples :rtype: int of tuple of str r)r2list)relrrrarityhs rBcsTeZdZdZfddZddZddZedd Zed d Z e d d Z Z S) Valuationa A dictionary which represents a model-theoretic Valuation of non-logical constants. Keys are strings representing the constants to be interpreted, and values correspond to individuals (represented as strings) and n-ary relations (represented as sets of tuples of strings). An instance of ``Valuation`` will raise a KeyError exception (i.e., just behave like a standard dictionary) if indexed with an expression that is not in its list of symbols. csnt|D]-\}}t|tst|tr|||<qt|tr&t|||<qtjd||fdd}t |dS)z= :param xs: a list of (symbol, value) pairs. zGError in initializing Valuation. Unrecognized value for symbol '%s': %sB)widthN) super__init__r-r:boolr9r?textwrapfillr6)selfZxssymvalmsg __class__rrrGs    zValuation.__init__cC ||vr t||Std|)NzUnknown expression: '%s'r" __getitem__rrKkeyrrrrS  zValuation.__getitem__cCst|Sr,rrKrrr__str__szValuation.__str__cCsNg}|D]}t|tr||qt|ts"|dd|Dqt|S)z7Set-theoretic domain of the value-space of a Valuation.cSs"g|] }|D]}|dur|qqSr,r)r/tuple_r>rrr s"z$Valuation.domain..)valuesr-r:appendrHextendr9)rKdomrMrrrdomains     zValuation.domaincCs t|S)z9The non-logical constants which the Valuation recognizes.)sortedkeysrWrrrsymbolss zValuation.symbolscCst|Sr,)read_valuation)clsr7rrr fromstringszValuation.fromstring) rrr__doc__rGrSrXpropertyr_rb classmethodre __classcell__rrrOrrCss   rCz \s*=+>\s*z\s*,\s*zg\s* (\([^)]+\)) # tuple-expression \s*cCst|}|d}|d}|drB|dd}t|}|r9g}|D]}|dd}tt|}||q#nt|}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_REr\r9)r7piecessymbolvalueZ tuple_stringsZ set_elementstselementrrr_read_valuation_lines       rxc Cs|dur ||}g}t|D]2\}}|}|ds"|dkr#qz |t|WqtyC}z td|d||d}~wwt|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 splitlinesstripror\rxr6rC)r7encodingZ statementsZlinenumlineerrrrcs rccsTeZdZdZdfdd 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||_|r-|D] \}}||jvsJd||jt|s(Jd||||<q d|_|dS)Nz'{}' is not in the domain: {}-Wrong format for an Individual Variable: '%s')rFrGr_formatrvariant _addvariant)rKr_ZassignvarrMrOrrrG0s     zAssignment.__init__cCrQ)Nz"Not recognized as a variable: '%s'rRrTrrrrS@rVzAssignment.__getitem__cCst|j}|||Sr,)rr_update)rKr=rrrcopyFs  zAssignment.copycCs |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)rKrrrrpurgeKs zAssignment.purgecCs6d}t|j}|D]\}}|d|d|d7}q |S)zQ Pretty printing for assignments. {'x', 'u'} appears as 'g[u/x]' g[/])r`r)rKZgstringrrMrrrrrXYs   zAssignment.__str__cCs6g}|D]}|d|df}||q||_dS)zK Create a more pretty-printable version of the assignment. rjrN)r&r\r)rKlist_r+pairrrrrds   zAssignment._addvariantcCsF||jvsJ|d|jt|sJd||||<||S)zh Add a new variable-value pair to the assignment, and update ``self.variant``. z is not in the domain r)r_rr)rKrrMrrrr;os zAssignment.addr,) rrrrfrGrSrrrXrr;rirrrOrrs4   rc@sPeZdZdZddZddZddZdd d Zdd d ZdddZ dddZ 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*. cCs<t|tsJ||_||_||jstd|j|fdS)NzDThe valuation domain, %s, must be a subset of the model's domain, %s)r-r9r_ valuation issupersetr)rKr_rrrrrGs zModel.__init__cCsd|jd|jdS)N(z, )r_rrWrrr__repr__szModel.__repr__cCsd|jd|jS)Nz Domain = z, Valuation = rrWrrrrXsz Model.__str__NcCsxz"t|}|j|||d}|r ttd|d|d||WSty;|r8ttd|d|YdSw)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 resatisfyr%r)rKexprrrparsedrurrrevaluates  zModel.evaluatecsvt|tr8|\}}t|tr&|}tfdd|D}||vS|j}|j}||St|trE|j  St|t rX|j oW|j St|t rk|j pj|j St|tr|j  p~|j St|tr|j |j kSt|tr|j |j kSt|trȈ} jD]} | |jj| |j | sdSqdSt|tr} jD]} | |jj| |j | rdSqdSt|tr} jD]} | |jj| |j | r dSqdSt|tr4i} |jj} jD]} |j | | } | | | <q| 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. c3s|] }|VqdSr,)rr/argrrKrrr1sz Model.satisfy..FT)r-rZuncurryrrr.functionargumentrtermrfirstsecondrr r r rrr_r;variablenamer rri)rKrrrr argumentsfunvalZargvalsargvalnew_gucfrrMrrrrsj                   z Model.satisfyFcCs@|jj|jjvr|j|jjSt|tr||jjStd|)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)rrrrbr-rr)rKrrrrrrrs    zModel.irc Cs6d}|||}g}t|trt|} n|} | |vr|r/tt||d|d||jD]U} |} | | j| |rJ|dkrJ|d} nd} | || | } |r]t|d| | dkrq|rpt|d|d | d q2| | |rt|d|d | d | q2d d |D}|St | jd|)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 rjrz(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-r:rfreer%r_rr;rrr\r)rKrZvarexrrZnestingZspacerindent candidatesrrrZlowtraceruresultrrr satisfierssD        zModel.satisfiersr,)F)Nr) rrrrfrGrrXrrrrrrrrr|s    Lrc Cstgdatatttattattdt tdtdt tdttdttdt gd}|D]}|rLtt |t|q=td|dt |tq=d 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) rCZval1r9Zdom1rm1rg1r%multr)rZ sentencessentrrrpropdemo_s&      rFc Csddddddhfddd hfd d hfd hd fgattatjatttattddga|st t dt t dt dt t dddtt dtgd}dd|D}t |D]}zt d|t |tfWq\t y{t d|Yq\wgd}|D];\}}z"t t |t}tdd|D} t |d|d| |vWqt yt |d|d Yqwd!Sd!S)"zExample of a first-order model.)adamb1)Zbettyr)Zfidod1girlrg2boyrb2dogrlove>)rr)rr)rr)rr)xr)yrrz Models Demoz Model m2: z-------------- zVariable assignment = )rrrwalksrrzcSg|]}t|qSrr re)r/rrrrrZzfolmodel..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 rerrrrrr1s zfolmodel..rz) evaluates to z) evaluates to UndefinedN)v2rCZval2r_Zdom2rrrrr%rrrr rer.) quietrexprsZ parsed_exprsrZ applicationsZfunr(rZargsvalrrrfolmodelsV            rc Cs~tddttdttdtdtgd}|D]}t|r.t|t|qtd|dt|tqdS) 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%rrrrr)rformulasfmlarrrfoldemos   rc Csttdttdtdttddgd}|r"tt|D] }t|t|q$dd|D}|D]}ttd|t |d t|q9d S) z5Satisfiers of an open formula in a first order model.rzSatisfiers DemoTr)zboy(x)z(x = x)z(boy(x) | girl(x))z(boy(x) & girl(x))z love(adam, x)z love(x, adam)z -(x = adam)zexists z22. love(x, z22)exists y. love(y, x)zall y. (girl(y) -> love(x, y))zall y. (girl(y) -> love(y, x))z)all y. (girl(y) -> (boy(x) & love(y, x)))z)(boy(x) & all y. (girl(y) -> love(x, y)))z)(boy(x) & all y. (girl(y) -> love(y, x)))z+(boy(x) & exists y. (girl(y) & love(y, x)))z(girl(x) -> dog(x))zall y. (dog(y) -> (x = y))rz&exists y. (love(adam, y) & love(y, x))cSrrr)r/rrrrrZrzsatdemo..zThe satisfiers of '{}' are: {}rN) r%rrrr rerrrr)rrrrprrrsatdemos$    rcCsPttttd}z |||dWdSty'|D] }|||dqYdSw)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 )rjrN)rrrrKeyError)numrZdemosrrrdemo(s  r__main__rrr,)FN)rN)3rfr resysrIpprintrZnltk.decoratorsrZnltk.sem.logicrrrrr r r r r rrrrrrr Exceptionrrrr8r?rBr"rCcompilermrrVERBOSErprxrcrrrrrrrrrrrrrsH   H  B  #_  1 < , 0