ó ù`]c@sÂdZddlmZmZddlmZddlmZddlm Z m Z ddl m Z m Z mZmZmZmZmZmZmZmZmZmZmZmZddlmZmZddlmZd efd „ƒYZ d „Z!d efd „ƒYZ"defd„ƒYZ#de$fd„ƒYZ%defd„ƒYZ&ede'fd„ƒYƒZ(d„Z)d„Z*d„Z+d„Z,d„Z-d„Z.d„Z/e0dkr¾e/ƒndS(uÆ A module to perform nonmonotonic reasoning. The ideas and demonstrations in this module are based on "Logical Foundations of Artificial Intelligence" by Michael R. Genesereth and Nils J. Nilsson. iÿÿÿÿ(tprint_functiontunicode_literals(t defaultdict(treduce(tProver9tProver9Command(tVariableExpressiontEqualityExpressiontApplicationExpressiont ExpressiontAbstractVariableExpressiont AllExpressiontBooleanExpressiontNegatedExpressiontExistsExpressiontVariablet ImpExpressiont AndExpressiontunique_variabletoperator(tProvertProverCommandDecorator(tpython_2_unicode_compatibletProverParseErrorcBseZRS((t__name__t __module__(((s:lib/python2.7/site-packages/nltk/inference/nonmonotonic.pyR)scCsC|dkr|}n|| g}ttjd„|DƒtƒƒS(Ncss|]}|jƒVqdS(N(t constants(t.0ta((s:lib/python2.7/site-packages/nltk/inference/nonmonotonic.pys 2s(tNoneRRtor_tset(tgoalt assumptionstall_expressions((s:lib/python2.7/site-packages/nltk/inference/nonmonotonic.pyt get_domain-s  tClosedDomainProvercBs)eZdZd„Zd„Zd„ZRS(u] This is a prover decorator that adds domain closure assumptions before proving. cCscg|jjƒD] }|^q}|jjƒ}t||ƒ}g|D]}|j||ƒ^qGS(N(t_commandR!R R#treplace_quants(tselfRR!R tdomaintex((s:lib/python2.7/site-packages/nltk/inference/nonmonotonic.pyR!;s"cCs7|jjƒ}t||jjƒƒ}|j||ƒS(N(R%R R#R!R&(R'R R(((s:lib/python2.7/site-packages/nltk/inference/nonmonotonic.pyR AscCsRt|tƒrug|D]$}|jj|jt|ƒƒ^q}g|D]}|j||ƒ^qG}td„|ƒSt|tƒr²|j |j|j |ƒ|j|j |ƒƒSt|t ƒrÕ|j|j|ƒ St|t ƒrJg|D]$}|jj|jt|ƒƒ^që}g|D]}|j||ƒ^q}td„|ƒS|SdS(uÞ Apply the closed domain assumption to the expression - Domain = union([e.free()|e.constants() for e in all_expressions]) - translate "exists x.P" to "(z=d1 | z=d2 | ... ) & P.replace(x,z)" OR "P.replace(x, d1) | P.replace(x, d2) | ..." - translate "all x.P" to "P.replace(x, d1) & P.replace(x, d2) & ..." :param ex: ``Expression`` :param domain: set of {Variable}s :return: ``Expression`` cSs||@S(N((txty((s:lib/python2.7/site-packages/nltk/inference/nonmonotonic.pytVtcSs||BS(N((R*R+((s:lib/python2.7/site-packages/nltk/inference/nonmonotonic.pyR,cR-N(t isinstanceR ttermtreplacetvariableRR&RR t __class__tfirsttsecondR R(R'R)R(tdt conjunctstct disjuncts((s:lib/python2.7/site-packages/nltk/inference/nonmonotonic.pyR&Fs 1%1%(RRt__doc__R!R R&(((s:lib/python2.7/site-packages/nltk/inference/nonmonotonic.pyR$5s  tUniqueNamesProvercBseZdZd„ZRS(u[ This is a prover decorator that adds unique names assumptions before proving. c Cs+|jjƒ}tt|jjƒ|ƒƒ}tƒ}xI|D]A}t|tƒr=|jj }|j j }||j |ƒq=q=Wg}x˜t |ƒD]Š\}}x{||dD]k} | ||kr°tt |ƒt | ƒƒ} tƒj| |ƒr ||j | ƒq|j| ƒq°q°Wq•W||S(u¦ - Domain = union([e.free()|e.constants() for e in all_expressions]) - if "d1 = d2" cannot be proven from the premises, then add "d1 != d2" i(R%R!tlistR#R t SetHolderR.RR3R1R4taddt enumerateRRtprovetappend( R'R!R(teq_setsRtavtbvtnew_assumptionstitbtnewEqEx((s:lib/python2.7/site-packages/nltk/inference/nonmonotonic.pyR!ns$    (RRR9R!(((s:lib/python2.7/site-packages/nltk/inference/nonmonotonic.pyR:hsR<cBseZdZd„ZRS(u& A list of sets of Variables. cCsVt|tƒst‚x|D]}||kr|SqWt|gƒ}|j|ƒ|S(uV :param item: ``Variable`` :return: the set containing 'item' (R.RtAssertionErrorRR@(R'titemtstnew((s:lib/python2.7/site-packages/nltk/inference/nonmonotonic.pyt __getitem__˜s   (RRR9RL(((s:lib/python2.7/site-packages/nltk/inference/nonmonotonic.pyR<“stClosedWorldProvercBs;eZdZd„Zd„Zd„Zd„Zd„ZRS(u¡ This is a prover decorator that completes predicates before proving. If the assumptions contain "P(A)", then "all x.(P(x) -> (x=A))" is the completion of "P". If the assumptions contain "all x.(ostrich(x) -> bird(x))", then "all x.(bird(x) -> ostrich(x))" is the completion of "bird". If the assumptions don't contain anything that are "P", then "all x.-P(x)" is the completion of "P". walk(Socrates) Socrates != Bill + all x.(walk(x) -> (x=Socrates)) ---------------- -walk(Bill) see(Socrates, John) see(John, Mary) Socrates != John John != Mary + all x.all y.(see(x,y) -> ((x=Socrates & y=John) | (x=John & y=Mary))) ---------------- -see(Socrates, Mary) all x.(ostrich(x) -> bird(x)) bird(Tweety) -ostrich(Sam) Sam != Tweety + all x.(bird(x) -> (ostrich(x) | x=Tweety)) + all x.-ostrich(x) ------------------- -bird(Sam) cCsÔ|jjƒ}|j|ƒ}g}x¥|D]}||}|j|ƒ}g|D]}t|ƒ^qQ}g} xf|jD][} g} x3t|| ƒD]"\} } | jt| | ƒƒq•W| jt d„| ƒƒqyWx_|j D]T}i}x+t||dƒD]\} } | || ùs(ttupletranget signature_len(R'RW((s:lib/python2.7/site-packages/nltk/inference/nonmonotonic.pyROôscCs-|}x |D]}|t|ƒƒ}q W|S(u† Return an application expression with 'predicate' as the predicate and 'signature' as the list of arguments. (R(R't predicatet signatureRaRY((s:lib/python2.7/site-packages/nltk/inference/nonmonotonic.pyRTûs cCs1ttƒ}x|D]}|j||ƒqW|S(uÏ Create a dictionary of predicates from the assumptions. :param assumptions: a list of ``Expression``s :return: dict mapping ``AbstractVariableExpression`` to ``PredHolder`` (Rt PredHoldert_map_predicates(R'R!RUR((s:lib/python2.7/site-packages/nltk/inference/nonmonotonic.pyRNs  c CsØt|tƒrM|jƒ\}}t|tƒrÔ||jt|ƒƒqÔn‡t|tƒr…|j|j|ƒ|j|j |ƒnOt|t ƒrÔ|j g}|j }x,t|t ƒr×|j |j ƒ|j }q¬Wt|tƒrÔt|jtƒrÑt|j tƒrÑ|jjƒ\}}|j jƒ\} } t|tƒrÎt| tƒrÎ|g|D]} | j ^q]krÎ|g| D]} | j ^qkrÎ|| jt|ƒ|jfƒ||j|ƒqÎqÑqÔndS(N(R.RtuncurryR t append_sigReRRkR3R4R R1R/R@Rt append_proptvalidate_sig_len( R't expressiontpredDicttfunctargsR[R/tfunc1targs1tfunc2targs2RY((s:lib/python2.7/site-packages/nltk/inference/nonmonotonic.pyRks0   "" (RRR9R!RORTRNRk(((s:lib/python2.7/site-packages/nltk/inference/nonmonotonic.pyRM§s  -  RjcBsDeZdZd„Zd„Zd„Zd„Zd„Zd„ZRS(uŸ This class will be used by a dictionary that will store information about predicates to be used by the ``ClosedWorldProver``. The 'signatures' property is a list of tuples defining signatures for which the predicate is true. For instance, 'see(john, mary)' would be result in the signature '(john,mary)' for 'see'. The second element of the pair is a list of pairs such that the first element of the pair is a tuple of variables and the second element is an expression of those variables that makes the predicate true. For instance, 'all x.all y.(see(x,y) -> know(x,y))' would result in "((x,y),('see(x,y)'))" for 'know'. cCsg|_g|_d|_dS(N(RPRRRRg(R'((s:lib/python2.7/site-packages/nltk/inference/nonmonotonic.pyt__init__As  cCs!|j|ƒ|jj|ƒdS(N(RoRPR@(R'RX((s:lib/python2.7/site-packages/nltk/inference/nonmonotonic.pyRmFs cCs%|j|dƒ|jj|ƒdS(Ni(RoRRR@(R'tnew_prop((s:lib/python2.7/site-packages/nltk/inference/nonmonotonic.pyRnJscCsI|jdkr!t|ƒ|_n$|jt|ƒkrEtdƒ‚ndS(NuSignature lengths do not match(RgRtlent Exception(R'RX((s:lib/python2.7/site-packages/nltk/inference/nonmonotonic.pyRoNscCsd|j|j|jfS(Nu (%s,%s,%s)(RPRRRg(R'((s:lib/python2.7/site-packages/nltk/inference/nonmonotonic.pyt__str__TscCsd|S(Nu%s((R'((s:lib/python2.7/site-packages/nltk/inference/nonmonotonic.pyt__repr__Ws( RRR9RxRmRnRoR|R}(((s:lib/python2.7/site-packages/nltk/inference/nonmonotonic.pyRj0s     c Cs–tj}|dƒ}|dƒ}|dƒ}t|||gƒ}t|jƒƒt|ƒ}tdƒx!|jƒD]}td|ƒquWtd|jƒƒt|jƒƒ|dƒ}|dƒ}|dƒ}|dƒ}t||||gƒ}t|jƒƒt|ƒ}tdƒx!|jƒD]}td|ƒq*Wtd|jƒƒt|jƒƒ|dƒ}|dƒ}|dƒ}|dƒ}t||||gƒ}t|jƒƒt|ƒ}tdƒx!|jƒD]}td|ƒqßWtd|jƒƒt|jƒƒ|dƒ}|dƒ}|d ƒ}t|||gƒ}t|jƒƒt|ƒ}tdƒx!|jƒD]}td|ƒq…Wtd|jƒƒt|jƒƒ|d ƒ}|d ƒ}|d ƒ}|d ƒ}|dƒ} |dƒ}t|||||| gƒ}t|jƒƒt|ƒ}tdƒx!|jƒD]}td|ƒqXWtd|jƒƒt|jƒƒdS(Nuexists x.walk(x)u man(Socrates)uwalk(Socrates)u assumptions:u ugoal:u -walk(Bill)u walk(Bill)u all x.walk(x)u girl(mary)u dog(rover)uall x.(girl(x) -> -dog(x))uall x.(dog(x) -> -girl(x))uchase(mary, rover)u1exists y.(dog(y) & all x.(girl(x) -> chase(x,y)))(R t fromstringRtprintR?R$R!R ( tlexprtp1tp2R7tprovertcdpRtp3tp4tp5((s:lib/python2.7/site-packages/nltk/inference/nonmonotonic.pytclosed_domain_demo[sz                               cCshtj}|dƒ}|dƒ}|dƒ}t|||gƒ}t|jƒƒt|ƒ}tdƒx!|jƒD]}td|ƒquWtd|jƒƒt|jƒƒ|dƒ}|dƒ}|d ƒ}|d ƒ}t||||gƒ}t|jƒƒt|ƒ}tdƒx!|jƒD]}td|ƒq*Wtd|jƒƒt|jƒƒdS( Nu man(Socrates)u man(Bill)uexists x.exists y.(x != y)u assumptions:u ugoal:u!all x.(walk(x) -> (x = Socrates))uBill = Williamu Bill = Billyu-walk(William)(R R~RRR?R:R!R (R€RR‚R7RƒtunpRR…((s:lib/python2.7/site-packages/nltk/inference/nonmonotonic.pytunique_names_demo s0            c Cs;tj}|dƒ}|dƒ}|dƒ}t|||gƒ}t|jƒƒt|ƒ}tdƒx!|jƒD]}td|ƒquWtd|jƒƒt|jƒƒ|dƒ}|dƒ}|d ƒ}|d ƒ}|d ƒ}t|||||gƒ}t|jƒƒt|ƒ}tdƒx!|jƒD]}td|ƒq9Wtd|jƒƒt|jƒƒ|d ƒ}|d ƒ}|dƒ}|dƒ}|dƒ}t|||||gƒ}t|jƒƒt|ƒ}tdƒx!|jƒD]}td|ƒqýWtd|jƒƒt|jƒƒdS(Nuwalk(Socrates)u(Socrates != Bill)u -walk(Bill)u assumptions:u ugoal:usee(Socrates, John)usee(John, Mary)u(Socrates != John)u(John != Mary)u-see(Socrates, Mary)uall x.(ostrich(x) -> bird(x))u bird(Tweety)u -ostrich(Sam)u Sam != Tweetyu -bird(Sam)(R R~RRR?RMR!R ( R€RR‚R7RƒtcwpRR…R†((s:lib/python2.7/site-packages/nltk/inference/nonmonotonic.pytclosed_world_demo½sL                    cCsŸtj}|dƒ}|dƒ}|dƒ}t|||gƒ}t|jƒƒttt|ƒƒƒ}x|jƒD]}t|ƒqwWt|jƒƒdS(Nusee(Socrates, John)usee(John, Mary)u-see(Socrates, Mary)( R R~RRR?R$R:RMR!(R€RR‚R7RƒtcommandR((s:lib/python2.7/site-packages/nltk/inference/nonmonotonic.pytcombination_prover_demoés    cCs†tj}g}|j|dƒƒ|j|dƒƒ|j|dƒƒ|j|dƒƒ|j|dƒƒ|j|dƒƒ|j|dƒƒ|j|dƒƒ|j|d ƒƒ|j|d ƒƒ|j|d ƒƒ|j|d ƒƒ|j|d ƒƒ|j|dƒƒtd|ƒ}tt|ƒƒ}x|jƒD]}t|ƒqGWt d|ƒt d|ƒt d|ƒdS(Nu'all x.(elephant(x) -> animal(x))u'all x.(bird(x) -> animal(x))u%all x.(dove(x) -> bird(x))u%all x.(ostrich(x) -> bird(x))u(all x.(flying_ostrich(x) -> ostrich(x))u)all x.((animal(x) & -Ab1(x)) -> -fly(x))u(all x.((bird(x) & -Ab2(x)) -> fly(x))u)all x.((ostrich(x) & -Ab3(x)) -> -fly(x))u#all x.(bird(x) -> Ab1(x))u#all x.(ostrich(x) -> Ab2(x))u#all x.(flying_ostrich(x) -> Ab3(x))u elephant(E)udove(D)u ostrich(O)u-fly(E)ufly(D)u-fly(O)( R R~R@RRR:RMR!Rt print_proof(R€tpremisesRƒRR((s:lib/python2.7/site-packages/nltk/inference/nonmonotonic.pytdefault_reasoning_demo÷s4      cCsPtj}t||ƒ|ƒ}tt|ƒƒ}t||jƒ|jƒƒdS(N(R R~RR:RMRR?(R RR€RƒR((s:lib/python2.7/site-packages/nltk/inference/nonmonotonic.pyR#s cCs'tƒtƒtƒtƒtƒdS(N(RˆRŠRŒRŽR‘(((s:lib/python2.7/site-packages/nltk/inference/nonmonotonic.pytdemo*s u__main__N(1R9t __future__RRt collectionsRt functoolsRtnltk.inference.prover9RRtnltk.sem.logicRRRR R R R R RRRRRRtnltk.inference.apiRRt nltk.compatRR{RR#R$R:R;R<RMtobjectRjRˆRŠRŒRŽR‘RR’R(((s:lib/python2.7/site-packages/nltk/inference/nonmonotonic.pyt s0^ 3+‰* E  ,  ,