B >?[d@sdZddlmZmZddlmZddlZddlZddlZddl Z ddl m Z ddl m Z ddlmZddlmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZGd d d e Z!Gd d d e!Z"d dZ#ddZ$ddZ%ddZ&eGddde'Z(e)dZ*e)dZ+e)dej,Z-ddZ.d1ddZ/eGddde'Z0eGd d!d!e1Z2d"Z3d2d#d$Z4d3d&d'Z5d4d(d)Z6d5d*d+Z7d6d,d-Z8e9d.kre8d/dd0dS)7zK This module provides data structures for representing first-order models. )print_functionunicode_literals)pformatN) string_types) decorator)python_2_unicode_compatible)AbstractVariableExpression AllExpression Expression AndExpressionApplicationExpressionEqualityExpressionExistsExpression IffExpression ImpExpressionIndividualVariableExpressionLambdaExpressionNegatedExpression OrExpressionVariable is_indvarc@s eZdZdS)ErrorN)__name__ __module__ __qualname__rr0lib/python3.7/site-packages/nltk/sem/evaluate.pyr0src@s eZdZdS) UndefinedN)rrrrrrrr4srcOsptjddkrt|}n t|}tt|d|}|ddrftx| D]}td|qRW|||S)Nrtracez%s => %s) sys version_infoinspectZgetfullargspecZ getargspecdictzippopprintitems)fargskwZargspecditemrrrr8s   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|tVqdS)N) isinstancetuple).0Zelrrr Qszis_rel..z.Set %r contains sequences of different lengthsN)lenallmaxmin ValueError)srrris_relEs *r7cCsTt}xH|D]@}t|tr(||fq t|trB|t|q ||q W|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-raddintstr)r6newelemrrrset2relWs    r>cCs t|dkrdStt|dS)ze Check the arity of a relation. :type rel: set of tuples :rtype: int of tuple of str r)r1list)Zrelrrrarityos 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. csxtt|xd|D]\\}}t|ts0t|tr:|||<qt|trRt|||<qtj d||fdd}t |qWdS)z= :param xs: a list of (symbol, value) pairs. zGError in initializing Valuation. Unrecognized value for symbol '%s': %sB)widthN) superrA__init__r-rboolr8r>textwrapZfillr5)selfZxsZsymvalmsg) __class__rrrEs  zValuation.__init__cCs$||krt||Std|dS)NzUnknown expression: '%s')r# __getitem__r)rHkeyrrrrLs zValuation.__getitem__cCst|S)N)r)rHrrr__str__szValuation.__str__cCsRg}xD|D]8}t|tr(||qt|ts|dd|DqWt|S)z7Set-theoretic domain of the value-space of a Valuation.cSs"g|]}|D]}|dk r |q qS)Nr)r/Ztuple_r=rrr sz$Valuation.domain..)valuesr-rappendrFextendr8)rHZdomrIrrrdomains   zValuation.domaincCs t|S)z9The non-logical constants which the Valuation recognizes.)sortedkeys)rHrrrsymbolsszValuation.symbolscCst|S)N)read_valuation)clsr6rrr fromstringszValuation.fromstring) rrr__doc__rErLrNpropertyrSrV classmethodrY __classcell__rr)rKrrAzs   rAz \s*=+>\s*z\s*,\s*zg\s* (\([^)]+\)) # tuple-expression \s*cCst|}|d}|d}|dr|dd}t|}|rvg}x<|D](}|dd}tt|}||qHWn 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_RErQr8)r6piecesZsymbolvalueZ tuple_stringsZ set_elementsZtselementrrr_read_valuation_lines       rjc Cs|dk r||}g}xlt|D]\\}}|}|ds$|dkrHq$y|t|Wq$tk r~td||fYq$Xq$Wt|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 %s: %s) decode enumerate splitlinesstriprcrQrjr5rA)r6encodingZ statementsZlinenumlinerrrrWs  rWcsTeZdZdZdfdd ZddZddZdd d Zd d Zd dZ ddZ Z S) Assignmentad A dictionary which represents an assignment of values to variables. An assigment 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 Ncsttt|||_|rbxH|D]@\}}||jksBtd||jft|sVtd||||<qWd|_|dS)Nz'%s' is not in the domain: %sz-Wrong format for an Individual Variable: '%s')rDrsrErSAssertionErrorrvariant _addvariant)rHrSZassignvarrI)rKrrrE9s    zAssignment.__init__cCs$||krt||Std|dS)Nz"Not recognized as a variable: '%s')r#rLr)rHrMrrrrLIs zAssignment.__getitem__cCst|j}|||S)N)rsrSupdate)rHr<rrrcopyOs  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)clearrv)rHrwrrrpurgeTs zAssignment.purgecCs4d}t|j}x |D]\}}|d||f7}qW|S)zQ Pretty printing for assignments. {'x', 'u'} appears as 'g[u/x]' gz[%s/%s])rTru)rHZgstringrurIrwrrrrNbs  zAssignment.__str__cCs:g}x*|D]}|d|df}||qW||_dS)zK Create a more pretty-printable version of the assignment. r^rN)r'rQru)rHZlist_r,Zpairrrrrvms zAssignment._addvariantcCsD||jkstd||jft|s0td||||<||S)zh Add a new variable-value pair to the assignment, and update ``self.variant``. z%s is not in the domain %sz-Wrong format for an Individual Variable: '%s')rSrtrrv)rHrwrIrrrr9xs zAssignment.add)N)N) rrrrZrErLryr{rNrvr9r]rr)rKrrss4   rsc@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|tst||_||_||js8td|j|fdS)NzDThe valuation domain, %s, must be a subset of the model's domain, %s)r-r8rtrS valuation issupersetr)rHrSr~rrrrEs zModel.__init__cCsd|j|jfS)Nz(%r, %r))rSr~)rHrrr__repr__szModel.__repr__cCsd|j|jfS)NzDomain = %s, Valuation = %s)rSr~)rHrrrrNsz Model.__str__NcCsny:t|}|j|||d}|r8ttd|||f|Stk rh|rdttd||fdSXdS)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' )rz '%s' evaluates to %s under M, %sz'%s' is undefined under M, %srN)r rYsatisfyr&r)rHexprr|rparsedrhrrrevaluates  zModel.evaluatecsPt|trt|\}}t|trL|}tfdd|D}||kS|j}|j}||Snt|tr|j  St|t r|j o|j St|t rڈ|j p؈|j St|tr|j  p|j St|tr.|j |j kSt|trV|j |j kSt|tr} x4jD]*} | |jj| |j | srdSqrWdSt|tr} x4jD]*} | |jj| |j | rdSqWdSt|tr>i} |jj} x.jD]$} |j | | } | | | <qW| S||SdS)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|]}|VqdS)N)r)r/arg)r|rHrrr0sz Model.satisfy..FTN)r-r Zuncurryrrr.functionZargumentrZtermr firstsecondrrrr r ryrSr9variablenamerri)rHrr|rrZ argumentsfunvalZargvalsZargvalnew_guZcfrwrIr)r|rHrrsV                    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)rrr~rVr-rr)rHrr|rrrrrs   zModel.ircCs.d}|||}g}t|tr(t|} n|} | |kr|r\tt||d||fx|jD]} |} | | j| |r|dkr|d} nd} | || | } |rt|d| | dkr|rt|d|| fqd| | |rdt|d|| | fqdWt d d |D}nt d | j|f|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 z'Open formula is '%s' with assignment %sr^rz(trying assignment %s)Fzvalue of '%s' under %s is Falsezvalue of '%s' under %s is %scss|] }|VqdS)Nr)r/crrrr0Vsz#Model.satisfiers..z%s is not free in %s) r-rrZfreer&rSryr9rrrQr8r)rHrZvarexr|rZnestingZspacerindentZ candidatesrwrrZlowtracerhresultrrr satisfierssB        zModel.satisfiers)N)N)F)Nr) rrrrZrErrNrrrrrrrrr}s   E r}cCstdddgatgatttattattdt tdtdt tdttdttdt dd d d d d dddddddddddg}x>|D]6}|rtt |t|qtd|t |tfqWdS)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)zThe value of '%s' is: %sN) rAZval1r8Zdom1r}Zm1rsg1r&multr)rZ sentencesZsentrrrpropdemofsD      rFc Csddddtddgfdtdd gfd td gfd td dddgfgattatjatttattddga |st t dt t dt dt t dddtt dt ddd ddddg}dd|D}t xL|D]D}yt d |t |t fWqt k rt d!|YqXqWd"d#d$d%g}xx|D]p\}}y>t t|t }td&d'|D} t d(||| |kfWn&t k rt d)||fYnXq4Wd*S)+zExample of a first-order model.)adamb1)Zbettyr)Zfidod1Zgirlrg2boyrb2Zdogrlove)rr)rr)rr)rr)xr)yrrz Models Demoz Model m2: z-------------- zVariable assignment = rwalksrrzcSsg|]}t|qSr)r rY)r/errrrOszfolmodel..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|tVqdS)N)m2rr rYr)r/rrrrr0szfolmodel..z%s(%s) evaluates to %sz%s(%s) evaluates to UndefinedN)r8Zv2rAZval2rSZdom2r}rrsrr&rrrr rYr.) quietrZexprsZ parsed_exprsrZ applicationsZfunr)rZargsvalrrrfolmodelsN      rcCstddttdttdtdtddddd d d d d dddddddddg}x@|D]8}t|r~t|t|q^td|t|tfq^WdS)zF Interpretation of closed expressions in a first-order model. T)rrzFOL 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))zThe value of '%s' is: %sN)rr&rrr{rr)rformulasfmlarrrfoldemos8    rcCsttdttdtdttddddddd d d d d ddddddddd dg}|rfttx|D]}t|t|qlWdd|D}x0|D](}ttd|t|dt|fqWdS)z5Satisfiers of an open formula in a first order model.rzSatisfiers DemoT)rzboy(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|qSr)r rY)r/rrrrrO&szsatdemo..zThe satisfiers of '%s' are: %srN) r&rrrr rYrr{r)rrrrprrrsatdemosB     rcCsVttttd}y|||dWn0tk rPx|D]}|||dq6WYnXdS)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^r)rN)rrrrKeyError)ZnumrZdemosrrrdemo-s  r__main__r)r)N)N)FN)N)N)rN):rZZ __future__rrZpprintrr"rGrer ZsixrZnltk.decoratorsrZ nltk.compatrZnltk.sem.logicrr r r r r rrrrrrrrr Exceptionrrrr7r>r@r#rAcompilerarfVERBOSErdrjrWrsobjectr}rrrrrrrrrrrsN    D  B  #   ] 1 < , .