{ "paper_id": "P85-1014", "header": { "generated_with": "S2ORC 1.0.0", "date_generated": "2023-01-19T09:39:15.241300Z" }, "title": "New Approaches to Parsing Conjunctions Using Prolog Sand,way Fong", "authors": [ { "first": "Robert", "middle": [ "C" ], "last": "Berwick", "suffix": "", "affiliation": { "laboratory": "Artificial hitelligence Laboratory M.I.T. 545 Technology Square C", "institution": "", "location": { "addrLine": "'umbridge MA 02t39", "country": "U.S.A" } }, "email": "" } ], "year": "", "venue": null, "identifiers": {}, "abstract": "Conjunctions are particularly difficult to parse in traditional, phra.se-based gramniars. This paper shows how a different representation, not b.xsed on tree structures, markedly improves the parsing problem for conjunctions. It modifies the union of phra.se marker model proposed by GoodalI [19811, where conjllnction is considered as tile linearization of a three-dimensional union of a non-tree I),'med phrase marker representation. A PItOLOG grantm~tr for conjunctions using this new approach is given. It is far simpler and more transparent than a recent phr~e-b~qed extraposition parser conjunctions by Dahl and McCord [1984]. Unlike the Dahl and McCor, I or ATN SYSCONJ appr~ach, no special trail machinery i.~ needed for conjunction, beyond that required for analyzing simple sentences. While oi contparable \u00a2tficiency, the new ~tpproach unifies under a single analysis a host of related constructions: respectively sentences, right node raising, or gapping. Another ,'ulvanrage is that it is also completely reversible (without cuts), and therefore can be used to generate sentences. John and Mary went to tile pictures Ylimplc constituent coordhmtion Tile fox and tile hound lived in tile fox hole and kennel respectively CotJstit,wnt coordination \"vith r.he 'resp~ctively' reading John and I like to program in Prolog and Hope Simple constitmvR co~rdinatiou but c,~, have a collective or n.sp,~'tively reading John likes but I hate bananas ~)tl-c,mstitf~ent coordin,~tion Bill designs cars and Jack aeroplanes Gapping with 'resp,~ctively' reading The fox. the honnd and the horse all went to market Multiple c,mjunets *John sang loudly and a carol Violatiofl of coordination of likes *Wire (lid Peter see and tile car? V/o/atio/i of roisrdJ)l=lte str\u00a2/\u00a2'trlz'e constr.~int *1 will catch Peter and John might the car Gapping, hut componcztt ~cnlenccs c.ntain unlike auxiliary verbs ?Tire president left before noon and at 2. Gorbachev", "pdf_parse": { "paper_id": "P85-1014", "_pdf_hash": "", "abstract": [ { "text": "Conjunctions are particularly difficult to parse in traditional, phra.se-based gramniars. This paper shows how a different representation, not b.xsed on tree structures, markedly improves the parsing problem for conjunctions. It modifies the union of phra.se marker model proposed by GoodalI [19811, where conjllnction is considered as tile linearization of a three-dimensional union of a non-tree I),'med phrase marker representation. A PItOLOG grantm~tr for conjunctions using this new approach is given. It is far simpler and more transparent than a recent phr~e-b~qed extraposition parser conjunctions by Dahl and McCord [1984]. Unlike the Dahl and McCor, I or ATN SYSCONJ appr~ach, no special trail machinery i.~ needed for conjunction, beyond that required for analyzing simple sentences. While oi contparable \u00a2tficiency, the new ~tpproach unifies under a single analysis a host of related constructions: respectively sentences, right node raising, or gapping. Another ,'ulvanrage is that it is also completely reversible (without cuts), and therefore can be used to generate sentences. John and Mary went to tile pictures Ylimplc constituent coordhmtion Tile fox and tile hound lived in tile fox hole and kennel respectively CotJstit,wnt coordination \"vith r.he 'resp~ctively' reading John and I like to program in Prolog and Hope Simple constitmvR co~rdinatiou but c,~, have a collective or n.sp,~'tively reading John likes but I hate bananas ~)tl-c,mstitf~ent coordin,~tion Bill designs cars and Jack aeroplanes Gapping with 'resp,~ctively' reading The fox. the honnd and the horse all went to market Multiple c,mjunets *John sang loudly and a carol Violatiofl of coordination of likes *Wire (lid Peter see and tile car? V/o/atio/i of roisrdJ)l=lte str\u00a2/\u00a2'trlz'e constr.~int *1 will catch Peter and John might the car Gapping, hut componcztt ~cnlenccs c.ntain unlike auxiliary verbs ?Tire president left before noon and at 2. Gorbachev", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Abstract", "sec_num": null } ], "body_text": [ { "text": "The problem addressed in this paper ~s to construct ,~ gr;unmatical device for lumdling cooL dination in natural language that is well founded in lingui.~tic theory and yet computationally attractive. 'the linguistic theory, should be powerful enough to describe ,~ll of the l)henomenon in coordi:tation, hut also constrained enough to reject all u.'lgr;unmatical examples without undue complications. It is difficult to ;tcldeve such ;t line h;dancc -cspcci,dly since the term grammatical itself is hil,hly subjccl.ive. Some examples of the kinds of phenolr-enon th:tt must l)e h;mdh.d are sh., '.wl hi fig. t '['he theory shouhl Mso be .~menable to computer hnpien:ellt~tion. For example, tilt represeuli~tion of the phrase, marker should be ,'onducive to Imth \u00a2le~u! process description antl efficient implementation of the associated operations as defined iu the linguistic theory.", "cite_spans": [ { "start": 596, "end": 610, "text": "'.wl hi fig. t", "ref_id": null } ], "ref_spans": [], "eq_spans": [], "section": "Introduction", "sec_num": null }, { "text": "The goal of the computer implementation is to prod,ce a device that can both generate surface sentences given ;t phrase inarker representation and derive a phrase marker represcnt;Ltion given a surface sentences. Thc huplementalion should bc ~ efficient as possible whilst preserving the essential properties of the linguistic theory. We will present an ir, ph:n,cut,'ttion which is transparent to the grammax and pcrliaps clemler & more nmdular than other systems such ,~ the int,:rpreter for the Modilh:r Structure Cram-,,,ar.~ (MSG.,) of l)alll & McCord [1983 I. \" ]'lie NISG systenl will be compared with ~ shnpliGed irnl)lenlenl.;~tion of tile proposed device. A table showin K tile execution thne of both systems for some sample sen-tences will be presented. Furthermore, the ,'ulvantages and disadvantages of our device will be discussed in relation to the MSG implementation.", "cite_spans": [ { "start": 517, "end": 567, "text": "Cram-,,,ar.~ (MSG.,) of l)alll & McCord [1983 I. \"", "ref_id": null } ], "ref_spans": [], "eq_spans": [], "section": "Fig 1: Example Sentences", "sec_num": null }, { "text": "Finally we can show how the simplifled device can l)e extended to deal with the issues of extending the system to handle nmltiple conjuncts ~d strengthening the constraints of the system. This representation of a phrase marker is equivalent to a proper subset of the more common syaxtactic tree representation. This means that some trees may not be representable by an RPM and all RPMs may be re-cast as trees. (For exmnple, trees wit.h shared nodes representing overlapping constituents are not allowed.) An example of a valid RPM is given in fig. 3 :-", "cite_spans": [], "ref_spans": [ { "start": 544, "end": 550, "text": "fig. 3", "ref_id": null } ], "eq_spans": [], "section": "Fig 1: Example Sentences", "sec_num": null }, { "text": "The phrase marker representation used by the theory described in the next section is essentially that of the Re- 'mnik & Kupin [1977] . A reduced phrase maxker c,'m be thought of im a set consist-\" ing of monostrings ,'rod a termiual striltg satisfying certain predicates. More formally, we haws ", "cite_spans": [ { "start": 113, "end": 133, "text": "'mnik & Kupin [1977]", "ref_id": null } ], "ref_spans": [], "eq_spans": [], "section": "The RPM Representation", "sec_num": null }, { "text": "duced Phrase Marker (RPM) of L,", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "The RPM Representation", "sec_num": null }, { "text": "Let E and N denote the set of terminals and non-terminals respectively.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Fig 3: Aa example of RPM representation", "sec_num": null }, { "text": "Let ~o,~, x E: (TI. U N)'. Let z, y, z E Z'. Let A be a single non-terminal. Let P be an arbitrary set.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Fig 3: Aa example of RPM representation", "sec_num": null }, { "text": "Then ~o is a monostrmg w.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Fig 3: Aa example of RPM representation", "sec_num": null }, { "text": "r.t. ~ & N if ~o E Z'.N.E'.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Fig 3: Aa example of RPM representation", "sec_num": null }, { "text": "Suppose~o = zAz and that ~o,$6:P where P is a some set of strings. We can also define the following predicates :yisa*~oin PifxyzEP dominates ~b in P if ~b = zXy. X # 0 and", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Fig 3: Aa example of RPM representation", "sec_num": null }, { "text": "x#A. W precedes v) in P if 3y s.t. y isa* ~o in P. ~b=zvX and X#z. ", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Fig 3: Aa example of RPM representation", "sec_num": null }, { "text": "This RPM representation forms the basis of i, he linguistic theory described in the next section. The set representation ha.s some dcsir;d~M advantages over a tree representation in terms of b.th simplicity of description and implementation of the operations.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "119", "sec_num": null }, { "text": "Goodall's idea in his draft thesis [Goodall??] wa.s to ext,md the definition of I.a.snik ~md t(upin's RPM to cover coordiuation. The main idea behind this theory is to apply tilt. notion that coordination remdts from *he union of phr,~e markers to the reduced I)hrmse marker. Since R PMs axe sets, this h,'m the desirable property that the union of RI'Ms wouhl just be the falltiliar set union operation. For a computer intplemeutation, the set union operation can be realized inexpensively. In contr,-Lst, the corresponding operation for trees would necessitate a much less simple and efficient union operation than set union.", "cite_spans": [ { "start": 35, "end": 46, "text": "[Goodall??]", "ref_id": null } ], "ref_spans": [], "eq_spans": [], "section": "Goodall's Theory of Coordination", "sec_num": null }, { "text": "However, the original definition of the R.PM did not ~nvisage the union operation necessary for coordination. \"['he RPM w~ used to represent 2-dimensional structure only. But under set union the RPM becomes a representation of 3-dimensional structure. The admissibility predicates dominates zmd precedes delined on a set of monustrings with a single non-terminal string were inadequate to describe 3-dimensional structure. B;~ically, Goodall's original idea w~ to extend the dominates ~m(l precedes predicates to handle RPMs under the set union operation. This resulted in the relations e-dominates ,'rod e-precedes ,xs shown in fig This extended definition, in particular -the notion of equivalence forms the baals of the computational device described in the next section, llowever since the size of\" the RPM may be large, a direct implementation of the above definition of equivMence is not computationMly fe,'tsible. In the actual system, an optimized but equivalent alternative definition is used.", "cite_spans": [], "ref_spans": [ { "start": 629, "end": 632, "text": "fig", "ref_id": null } ], "eq_spans": [], "section": "Goodall's Theory of Coordination", "sec_num": null }, { "text": "Although these definitions suffice for most examples of coordination, it is not sufficiently constrained enough to reject stone ungr,'mzmatical examples. For exaanple, fig. 5 gives the RPM representation of \"*John sang loudly and a carol\" in terms of the union of the RPMs for the two constituent sentences :- The above example indicates that the extended RPM definition of Goodall Mlows some ungrammatical sentences to slip through. Although the device preseuted in the next section doesn't make direct use of the extended definitions, the notion of equivMence is central to the implementation. The basic system described in the next section does have this deficiency but a less simplistic version described later is more constrained -at the cost of some computational efficiency.", "cite_spans": [], "ref_spans": [ { "start": 168, "end": 174, "text": "fig. 5", "ref_id": "FIGREF5" } ], "eq_spans": [], "section": "Goodall's Theory of Coordination", "sec_num": null }, { "text": "Although a theory of coordination ham been described in the previous sections -in order for the theory to be put into practice, there remain two important questions to be answered :-", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Linearization and Equivalence", "sec_num": null }, { "text": "\u2022 I-low to produce surface strings from a set of sentences to be conjoined?", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Linearization and Equivalence", "sec_num": null }, { "text": "\u2022 tlow to produce a set of simple sentences (i.e. sentences without co,junct.ions) from ~ conjoined surface string?", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Linearization and Equivalence", "sec_num": null }, { "text": "This section will show that the processes ot\" //n-e~zation and finding equivalences provide an answer to both questions. For simplicity in the following discussion, we assume that the number of simple sentences to be conjoined is two only.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Linearization and Equivalence", "sec_num": null }, { "text": "The processes of linearization ~md 6riding equivalences for generation can be defined as :-Given a set of sentences and a set of candidates which represent the set of conjoinable pairs for those sentences, llnearizatinn will output one or more surface strings according to a fixed procedure.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Linearization and Equivalence", "sec_num": null }, { "text": "Given a set of sentences, findinff equivalences will prodnce a set o( conjoinable pairs according to the definition of equivalence o# the linguistic theory.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Linearization and Equivalence", "sec_num": null }, { "text": "[;'or genera.Lion the second process (linding equivalences) iu caJled first to generate a set of (:andidates which is then used in the first, process (linearization) to generate the s.rface strings. For parsing, the definitions still holdbut the processes are applied in reverse order.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Linearization and Equivalence", "sec_num": null }, { "text": "To illustrate the procedure for linearization, consider the following example of a set of simple sentences as given in the description of the extended RPM requires the general.ion of the combined R.PM of the constituent senlances. However it can be shown [I,'ong??] by considering the constraints impc,sed by the delinitions of equivalence and linc:trization, that tile same set of equivalent terminal string.~ can be produced just by using the terminal strings of the RI*M alone. There ;tre consider;Lble savings of compu-tatioaal resources in not having to compare every element of the set with every other element to generate all possible equivalent strings -which would take O(n ~) time -where n is the cardinality of the set. The corresponding term for the modified definition (given in the next sectiou) is O(1).", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Linearization and Equivalence", "sec_num": null }, { "text": "This section describes a runnable specification written in Prolog. The specification described also forms the basis for comparison with the MSG interpreter of Dahl aud Me-Cord. The syntax of the clauses to be presented is similar to the Dec-10 Prolog [Bowen et a1.19821 version. The main differences are :-", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "The Implementation in Prolog", "sec_num": null }, { "text": "\u2022 The symbols %\" and ~,\" have been replaced by the more meaningful reserved words \"if\" and \"and\" respectively.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "The Implementation in Prolog", "sec_num": null }, { "text": "\u2022 The symbol \".\" is used ,as the list constructor and \u2022 Cmnments (shown in italics) may be interspersed between tile argamaents in a clause.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "The Implementation in Prolog", "sec_num": null }, { "text": "In tile previous section tile processes of linearization and linding equivalences are described ;m tile two components necessary for parsing and generating conjoined sentestes. We will show how Lhese processes can be combined to produce a parser and a generator. as dellned by the procedure given in the previous section.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Parse and Generate", "sec_num": null }, { "text": "equivahmtpairs( X Y fi'om S1 $2)", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Parse and Generate", "sec_num": null }, { "text": "Equivalentpairs hohls when a ~uhstring X of S1 is equivalent to a substring Y of $2 accordhtg to the delinition of equivalence in the linguistic theory.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Parse and Generate", "sec_num": null }, { "text": "The definitions fi~r parsing ,'utd generating are almost logically equivalent. Ilowever the sub-goals for p~sing are in reverse order to the sub-goals for generatingsince the Prolog interpreter would attempt to solve the sub-goals in a left to right manner. Furthc'rmore, the subset relation rather than set equality is used in the definition for parsing. We can interpret the two definitions ~ follows ( fig. t2) ", "cite_spans": [], "ref_spans": [ { "start": 405, "end": 413, "text": "fig. t2)", "ref_id": "FIGREF2" } ], "eq_spans": [], "section": "Parse and Generate", "sec_num": null }, { "text": "Generate holds when Sentence is the conjoined sentence resulting/'ram the linearization of the pair of dilFerence lists (Sl. nil) and (52. Additionally, let the mete-logical predicate ~etof as in \"setof(l~lement Goal Set)\" hohl when Set is composed of chin,eats c~f the form Element anti that Set contains all in,: auccs of Element I, hat satisfy the goal Goal. The predicates generate can now be defined in terms of these two processes as folluws (lig. ", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": ":-", "sec_num": null }, { "text": "We can also fashion a logic specification for the process of line~tt'izatiou in the same manner. In this section we will describe the cases corresponding to each Prolog clause necessary in the specification of [inearization. However, ,'or sitnplicity the actual Prolog code is not shown here. (See Appendix A tbr the delinition of predicate Iinearize.)", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Linearize", "sec_num": null }, { "text": "Ill the following discussion we assume that tile template for predicate Iinearize has the form \"linearize( pairs Sl El and 52 E2 rand,tides Set gives Sentence)\" shown previously in tig. I0. There are three independent cases to con:rider durivg !incariz~tion ft. The Base Case.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Linearize", "sec_num": null }, { "text": "If the two ,lilrcrence tist~ ({S1. El} & {S2. E2}) are both empty then the conjoined string (Sentence) is also entpty. This siml,ly sta.tes that if two empty strings arc conjoint:d then the resttit is also an empty string.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Linearize", "sec_num": null }, { "text": "The second case occurs wheTt the two (non-eml)ty) difference lists have identical leading non-empty substrings. Then the coni-ined string is identical to the concatenation of that leading substring with the lin-eari~.ation of the rest of th,: two difference lists. For example, consider the linearization of the two flagments \"likes Mary\" and \"likes Jill\" as shown in fig. 13 ..", "cite_spans": [], "ref_spans": [ { "start": 368, "end": 375, "text": "fig. 13", "ref_id": null } ], "eq_spans": [], "section": "Identical Leading Substrlngs.", "sec_num": "2." }, { "text": "{likes Mary. likes Jill} which can be. lineariz~:", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Identical Leading Substrlngs.", "sec_num": "2." }, { "text": "d a~ :- {likes X}", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Identical Leading Substrlngs.", "sec_num": "2." }, { "text": "where X is the linearization of strings {Mary. Jill} l'Tg. 13: Example of identical leading substrings 3. Conjohfing. The last case occurs when the two pairs of (qonempty) difference lists have no common leading substring, llere, the conjoined string will be the co,tcatenation nf the co.junctinn of one of the pairs from the candidate set, with the conjoined sqring resulting fr~nl the line;trization of the two strings with their respective candidate substrings deleted. For example, consider the linearization -f the two sentences \"John likes Mary\" aitd \"Bill likes Jill\" a~ shown in fig. 14 Given th,t the .~elertt:,l ,',ltdi,l,tc lmir is {John. Bill}, the c,,sj,,,',,:,l :;,rtdt ,,'e ~;:,ul. All of the strings ,'ire then passed to the predicate findequivalences which shouhl pick out the second pair of strings as the only grammatically correct linearization.", "cite_spans": [ { "start": 595, "end": 696, "text": "Given th,t the .~elertt:,l ,',ltdi,l,tc lmir is {John. Bill}, the c,,sj,,,',,:,l :;,rtdt ,,'e ~;:,ul.", "ref_id": null } ], "ref_spans": [ { "start": 587, "end": 594, "text": "fig. 14", "ref_id": "FIGREF4" } ], "eq_spans": [], "section": "Identical Leading Substrlngs.", "sec_num": "2." }, { "text": "(.;oodall's delinition of eqnivalence w,'~s that two terminal strings were said to be equivalent if they h;ul the same left and right contexts. Furthermore we had previously a.ssertcd th;~t the equivaleut pairs couhl be l}roduced without ~earching the whole RI'M. For example consider the equivah.nt lernnimd strings in the two sentences \"Alice saw Bill\" an,J \"Mary saw Bill\" ( fig. 16 ) :-{John and Bill X.} where X is tl~e linearization of ~;trin~,s {likes Mary, likes .Jill} Fig. 1,1: [ ';xaml~ic of ,:,mj,iui,g ..mh.st, rin,,,,.,; There are S,.hC i,ul~h~,.c.t;dic.= d,:t;tils Lhat are dlfr,~re.t for parsi.g tc~ ge,er:ttinK. (~ec al~l~,ndi.'c A.) llowcver the fierce cases :u'e the sanonc for hoth.", "cite_spans": [ { "start": 490, "end": 534, "text": "';xaml~ic of ,:,mj,iui,g ..mh.st, rin,,,,.,;", "ref_id": null } ], "ref_spans": [ { "start": 378, "end": 385, "text": "fig. 16", "ref_id": null }, { "start": 478, "end": 489, "text": "Fig. 1,1: [", "ref_id": null } ], "eq_spans": [], "section": "Finding Equiwdences", "sec_num": null }, { "text": "We cast illusl, r;ll.e the :tl~\u00a2~v,; dc:llntili,m by she=wing x & y axe both nonempty. In the above example, x--nil and fl=\"saw Bill\", so the first a.ud the third pairs produced are redundant.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Finding Equiwdences", "sec_num": null }, { "text": "In general, a pair of terminal strings are redundant if they have the form (uv, uw) or (uv, zv) , in which case -they may be replaced by the pairs (v, w) ~ad (u, z) respectively.", "cite_spans": [ { "start": 75, "end": 95, "text": "(uv, uw) or (uv, zv)", "ref_id": null } ], "ref_spans": [], "eq_spans": [], "section": "Finding Equiwdences", "sec_num": null }, { "text": "\u2022 Ia Goodall's definition any two terminal strings themselves are also a pair of equivalent terminal strings ( whe, X & f2 ,are both ,ull) . We exclude this case it produces simple string concatenation of sentences.", "cite_spans": [ { "start": 109, "end": 138, "text": "( whe, X & f2 ,are both ,ull)", "ref_id": null } ], "ref_spans": [], "eq_spans": [], "section": "Finding Equiwdences", "sec_num": null }, { "text": "The above restrictions imply that in fig. 16 the only remai,ing equivalent pair ({Alice. Mary})is the correct one for tl, is example.", "cite_spans": [], "ref_spans": [ { "start": 37, "end": 44, "text": "fig. 16", "ref_id": null } ], "eq_spans": [], "section": "Finding Equiwdences", "sec_num": null }, { "text": "However, before fiuding eq,ivalent pairs for two simple zenlences, the ittocess ,,f fimli, g ,quiv.,lel, ces ,nlust check that the two se,tt,;nces ate actually gral,tlllatical. We ;msuune thnt a recot;nizer/i,arser (e.g. a predicate parse(S El) alremly exists for determining the grammaticality of ~itnple ~entenccs. Since the proct'ss only requires a yes/no answer to gramnmtic;dity, any parsing or recognition sysl.e;,t f,,r simple sentences can be used.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Finding Equiwdences", "sec_num": null }, { "text": "We can now specify a l,redicate lindcandi(lates(X Y SI $2) that hohls when {X. Y} is an equiw,hmt pair front the two grantmatical simple .:e,te,ces {SI. $2} .~ f, llows (li!,\u00a2. 17):findcandidates(X and Y in SI and $2) ir parse(Sl nil) ilnld parse(S2 nil) and eqlniv(X Y SL $2) wh,.rc eqt,iv is ,h 'fit~,'d as :. ~q.iv(X Y X1 YI) if append3(Chi X Omega Xl) and ternfinals(X) and append3(C.hi Y Omega YI) and terminals (Y) :vh, 'r, ' :q, t, ', , , IS(L! L2 I..'~ L 1) h, , hls wh, .n L.I i:\" , ', l, ml ; o th, . c', , tJ, 'nl, 't~; tli, , tl , , f I.I.L2 .~: 1.3. h'rminzd.~(X) holds when X i. '~ n li..t , , 1' t, 'rtztinnl .~yml, , , Is ouly Fig. l 7: Logic delit, itiolz .f Fi.:lcntldirh, Les Then the predicate findcquivalencos is simply defined ;t~ ( fig. 18 ) :-findequivalences(X and Y in S1 and $2) if findcandidates(X and Y in S1 and $2) and not redundant (X Y) wl.,re redundant implements the two restrictions described.", "cite_spans": [ { "start": 297, "end": 311, "text": "'fit~,'d as :.", "ref_id": null }, { "start": 417, "end": 425, "text": "(Y) :vh,", "ref_id": null }, { "start": 426, "end": 429, "text": "'r,", "ref_id": null }, { "start": 430, "end": 435, "text": "' :q,", "ref_id": null }, { "start": 436, "end": 438, "text": "t,", "ref_id": null }, { "start": 439, "end": 441, "text": "',", "ref_id": null }, { "start": 442, "end": 443, "text": ",", "ref_id": null }, { "start": 444, "end": 445, "text": ",", "ref_id": null }, { "start": 446, "end": 468, "text": "IS(L! L2 I..'~ L 1) h,", "ref_id": null }, { "start": 469, "end": 470, "text": ",", "ref_id": null }, { "start": 471, "end": 478, "text": "hls wh,", "ref_id": null }, { "start": 479, "end": 491, "text": ".n L.I i:\" ,", "ref_id": null }, { "start": 492, "end": 494, "text": "',", "ref_id": null }, { "start": 495, "end": 497, "text": "l,", "ref_id": null }, { "start": 498, "end": 502, "text": "ml ;", "ref_id": null }, { "start": 503, "end": 508, "text": "o th,", "ref_id": null }, { "start": 509, "end": 514, "text": ". c',", "ref_id": null }, { "start": 515, "end": 516, "text": ",", "ref_id": null }, { "start": 517, "end": 520, "text": "tJ,", "ref_id": null }, { "start": 521, "end": 525, "text": "'nl,", "ref_id": null }, { "start": 526, "end": 530, "text": "'t~;", "ref_id": null }, { "start": 531, "end": 535, "text": "tli,", "ref_id": null }, { "start": 536, "end": 537, "text": ",", "ref_id": null }, { "start": 538, "end": 542, "text": "tl ,", "ref_id": null }, { "start": 543, "end": 544, "text": ",", "ref_id": null }, { "start": 545, "end": 576, "text": "f I.I.L2 .~: 1.3. h'rminzd.~(X)", "ref_id": null }, { "start": 593, "end": 605, "text": "'~ n li..t ,", "ref_id": null }, { "start": 606, "end": 607, "text": ",", "ref_id": null }, { "start": 608, "end": 613, "text": "1' t,", "ref_id": null }, { "start": 614, "end": 630, "text": "'rtztinnl .~yml,", "ref_id": null }, { "start": 631, "end": 632, "text": ",", "ref_id": null }, { "start": 633, "end": 634, "text": ",", "ref_id": null }, { "start": 635, "end": 665, "text": "Is ouly Fig. l 7: Logic delit,", "ref_id": null }, { "start": 666, "end": 690, "text": "itiolz .f Fi.:lcntldirh,", "ref_id": null }, { "start": 691, "end": 694, "text": "Les", "ref_id": null } ], "ref_spans": [ { "start": 755, "end": 762, "text": "fig. 18", "ref_id": null }, { "start": 864, "end": 869, "text": "(X Y)", "ref_id": null } ], "eq_spans": [], "section": "Finding Equiwdences", "sec_num": null }, { "text": "The following table ( fig. 19) gives tile execution times in milliseconds for the parsing of some sample sentences mostly taken from Dahl 0~ McCor(l [1983] . Both systems were executed using Dec-20 Prolog. The times shown for the MSG interpreter is hazed on the time taken to parse ,'rod buihl the syntactic tree only -the time for the subsequent transformations w,-~s not ,,chided. From tile timings we can conclude that the propo..:ed device is comparable to the MSC, system in terms -f comt,ttati,Jn:d elllciency, llowever, there are some other advantages s,,ch as :-", "cite_spans": [ { "start": 133, "end": 155, "text": "Dahl 0~ McCor(l [1983]", "ref_id": null } ], "ref_spans": [ { "start": 22, "end": 30, "text": "fig. 19)", "ref_id": null } ], "eq_spans": [], "section": "Comparison with MSGs", "sec_num": null }, { "text": "\u2022 Transparency of the grammar -There is no need for phrmsal rules such .-m \"S ~ S and S\" The device also allows ,,m-phr~al conjunction.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Comparison with MSGs", "sec_num": null }, { "text": "* Since no special grammar or particular phr~e marker representation is required, any par.,;er can be usedthe dcvicc' only requires an acctpt/reject answer.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Comparison with MSGs", "sec_num": null }, { "text": "\u2022 The specification is uot biased with respect to liarsing or generation. The iniplement:ition is reversible allowing it to generate aay sentence it can parse and vice versa.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Comparison with MSGs", "sec_num": null }, { "text": "\u2022 Modularity of the device. The granimaticallty of sentestes with conjunctiou is determined by the definition of equivalence. For instance, if needed we can filter the equivalent terlninals using semantics.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Comparison with MSGs", "sec_num": null }, { "text": "It is worthwhile to compare the phr;me marker approach t{i the Aq.'N-ba.sed SYSCON.I inechanisln. Like SYSCONJ~ OUr analysis is extragrammatical: we do not tanlper with the h,sic gramnlar, but add a new cnniponent *.hat handles conjunction. Unlike SYSCONJ, our approach is based on a precise definition of \"equiwdent tlhrztse~\" that attenlpts ta unify urider one analysis nlany dill'erent types of coordination phen,mena. :~YSi~,ONJ relied ou a rather conipticated, interrupt-driven method that restarted sentence ~malysis in SOlltC previously recorded m;tchine coiilil~qiration, but with the input sequence following the conjunction. This capturcs part of the \"multillle planes\" analy:ds of the phrase marker ,'tpproach, but without a precise notion of equivalent phr,'l~es. Perhaps ~ a result, SYSCONJ handled only ordinary conjunction, ali(l [tot respectively or gapping read-ing~. In our appr-:,h, a simple change to the lincarization process allows ll~ t~l handle gapping.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "A Note on SYSCONJ", "sec_num": null }, { "text": "The device described in the previ,lus section is a .~iluplified version for rough elliilll;iristin wii.h the MS~ inter-In'ctct \". llowever, the systClll C;ill e.tsily he gciicralizcd to h~uidle nlultiple conjunctz. The only ,uhliti.nal phase required ia to gelicrate telnpl:tte~ for nluttlph: rc:ulings. Also, gallpillg can lie handled just lly adding clauses tll the deftnifioll of linearize -which allows :l dilferent path from that of fi~. 8 to be taken.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Extensions to the Basic Device", "sec_num": null }, { "text": "The ~iinlllilied device llVruiits ~llllil. ,.,(ainllh~s of ungr;liillii;lli\u00a2:tl ~.l.il!l,nfl.s I.,, h,r ll;U'<'ed as if tin'i--or (lig. 5), The inildularity ~f the systelll all.ws its {() ciln..itr;tin the dcliiiii.iclii of eClUiv:th,qlcl~ still I'lirl.hl.r. The c\u00d7tcndcl[ dellniticlns in (141~lthdl's draft l, hcory wci-e licit iiichilled iii his the-si~; (;,i,.la11144i lirP~lilll;lllly hl,vi'.liSe it w:us liill COli.'-itrailled en~liigh. Ilnwever in lii.~ I.hl~sis he lll'llll~lses illiolher :lefinition elf !4raniliial.ic;dity ilshil~ II.l~Ms. This delliiitilln cltn lie lisctl t.o c~liistrain i~Cliiiv.-tlclice .,;till I'ilrl, lier ill Clllr systelli at a lOSS fif Siillle crllil:ieni:y ;llld gelilrl';ilil.y. For (~Xltlll|ile, the n~quircd ;tdditional predicate will need to ni;tke explicit use of the colnbined RPM. Therefilre, a parser will need to produce a I1.PM representation as its phr,~ze marker. The modifications necessary to produce th,, representation is shown hi appemlix B.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Extensions to the Basic Device", "sec_num": null } ], "back_matter": [ { "text": "This work describes research clone at the Artificial Intelligence Laboratory of the Massachusetts Institute of Technology. Sitpport for the Laboratory's artificial intelligence rese,'u'ch has been provided in part by the Advanced Research Projects Agency of the Depitrtnlent of Defense under Office of Naval Re'~earch contract N000t-I-80-C-0505. The first author is also filndnd by a scholarship from the Kennedy Memorial Trust.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Acknowledgements", "sec_num": null }, { "text": "Thl\" fiill Pr.h~g Sll~.ilh.;iiilni flw thl, llrl.dicail , lineai'ize i~ givl.n lll.l(iw. / Linenrize f.r g~ 'ncr.tion / / tcrmin, din~) r.n, lition / liu('arizt'(pairs SI , I and $2 $2 candidates [,i.~t ,, ..,va,'(~,',tt(',tce) and :tl)l), ',,d: {(h,,,.ioi,te,} I, lh.stt)f:q,.,tt,.,,c,. ~/i,,in~ S,.ttLt.,,c\u00a2.) and , ',,,lj,,i,,(li.~l l'lh',,,,',,l ,t.~i,t!l ';o,,l\" :l,,,irtrJ ( h,ttj,hne, l) and ~illii,.( l';h.i,ii.,il. ,i. ", "cite_spans": [ { "start": 108, "end": 129, "text": "'ncr.tion / / tcrmin,", "ref_id": null }, { "start": 130, "end": 140, "text": "din~) r.n,", "ref_id": null }, { "start": 141, "end": 172, "text": "lition / liu('arizt'(pairs SI ,", "ref_id": null }, { "start": 173, "end": 184, "text": "I and $2 $2", "ref_id": null }, { "start": 196, "end": 202, "text": "[,i.~t", "ref_id": null }, { "start": 203, "end": 227, "text": ",, ..,va,'(~,',tt(',tce)", "ref_id": null }, { "start": 240, "end": 311, "text": "',,d: {(h,,,.ioi,te,} I, lh.stt)f:q,.,tt,.,,c,. ~/i,,in~ S,.ttLt.,,c\u00a2.)", "ref_id": null }, { "start": 318, "end": 394, "text": "',,,lj,,i,,(li.~l l'lh',,,,',,l ,t.~i,t!l ';o,,l\" :l,,,irtrJ ( h,ttj,hne, l)", "ref_id": null } ], "ref_spans": [], "eq_spans": [], "section": "Appendix A: Linearization", "sec_num": null } ], "bib_entries": { "BIBREF0": { "ref_id": "b0", "title": "Warre:l. Docsystem-lO Prolog User's Man-ira1", "authors": [], "year": null, "venue": "", "volume": "", "issue": "", "pages": "", "other_ids": {}, "num": null, "urls": [], "raw_text": "Bow~.n ~.t al: D.L. Bowo,l {ed.), L. Byrd, F.C.N. Pert,ira, L.M. P,,r(.ira, D.H.I). Warre:l. Docsystem-lO Prolog User's Man- ira1. Hniversity of Edinburgh. t982.", "links": null }, "BIBREF1": { "ref_id": "b1", "title": "Trcatiiig Coordination in Iaigie Gramtnars", "authors": [ { "first": ":", "middle": [ "V" ], "last": "Dahl F4 Mccord", "suffix": "" }, { "first": "M", "middle": [ "C" ], "last": "Dahl", "suffix": "" }, { "first": "", "middle": [], "last": "Mccord", "suffix": "" } ], "year": null, "venue": "Anit.ric~ui Journal of Compu-taii~lnal Linguistics", "volume": "9", "issue": "2", "pages": "", "other_ids": {}, "num": null, "urls": [], "raw_text": "Dahl f4 McCord: V. Dahl and M.C. McCord. Trcatiiig Coordi- nation in Iaigie Gramtnars. Anit.ric~ui Journal of Compu- taii~lnal Linguistics. Vol. 9. No. 2 (t983).", "links": null }, "BIBREF2": { "ref_id": "b2", "title": "Jrdinatioli ill L~lgic", "authors": [ { "first": "", "middle": [], "last": "Piing", "suffix": "" } ], "year": 1985, "venue": "", "volume": "", "issue": "", "pages": "", "other_ids": {}, "num": null, "urls": [], "raw_text": "Piing.')?: .%mdiway l\"ong. To appear in S,'t,L thesis -\".~pccifying C,,Jrdinatioli ill L~lgic\" -1985", "links": null }, "BIBREF4": { "ref_id": "b4", "title": "Draft -Chapter 3 (sections 2.1", "authors": [ { "first": "Grant", "middle": [], "last": "Todd", "suffix": "" }, { "first": "(", "middle": [ ";" ], "last": "", "suffix": "" } ], "year": null, "venue": "", "volume": "", "issue": "", "pages": "", "other_ids": {}, "num": null, "urls": [], "raw_text": "Grant Todd (;.,.lall. Draft -Chapter 3 (sections 2.1. to 2.7)-C,,irdination.", "links": null }, "BIBREF5": { "ref_id": "b5", "title": "~ : ( ;ralit To,hi (:oolhdl, P:lrnlh.l Strltctnr\u00a2,s iil ,~yiltax. Ph. D thesis. Uniw.rsity (if CMifiJruia", "authors": [ { "first": "", "middle": [], "last": "Goodall", "suffix": "" } ], "year": null, "venue": "", "volume": "", "issue": "", "pages": "", "other_ids": {}, "num": null, "urls": [], "raw_text": "Goodall.~.~ : ( ;ralit To,hi (:oolhdl, P:lrnlh.l Strltctnr\u00a2,s iil ,~yiltax. Ph. D thesis. Uniw.rsity (if CMifiJruia. San Di{.go (tO8, U.", "links": null }, "BIBREF6": { "ref_id": "b6", "title": "Kupin: I1. La.~uik iuid .I. [~upin. A r~'strictive th\u00a2,ory +Jt ir.'iosfi,r'.ilatiotl;d gr;Imiilar. Th('or~.tical I.inl4ui:itics ,I", "authors": [ { "first": "", "middle": [], "last": "Lasnik", "suffix": "" } ], "year": 1977, "venue": "", "volume": "", "issue": "", "pages": "", "other_ids": {}, "num": null, "urls": [], "raw_text": "Lasnik [.: Kupin: I1. La.~uik iuid .I. [~upin. A r~'strictive th\u00a2,ory +Jt ir.'iosfi,r'.ilatiotl;d gr;Imiilar. Th('or~.tical I.inl4ui:itics ,I (19771.", "links": null } }, "ref_entries": { "FIGREF0": { "text": "(fig. 2) :-Sentence: Alice saw 13ill RPM representation: {S. Alice.saw.Bill. NP.saw.Bill. Alice.V.Bill. Alice.VP.Alice.saw.NP}", "uris": null, "num": null, "type_str": "figure" }, "FIGREF1": { "text": "is an RPM if 3A,z s.t. A,z ~. P and V{~O,~0} C_ P then dominates ~o in P or ~o dominates ~b in P or ~b precedes ~ in P or ~,, precedes ~b in P.", "uris": null, "num": null, "type_str": "figure" }, "FIGREF2": { "text": "Delinitioa of azl RPM", "uris": null, "num": null, "type_str": "figure" }, "FIGREF3": { "text": ". 4 :-Assuming the definitions of fig. 2 and in addition let ~, f2, 0 E (~ O N)\" and q, r, s, t, u E ]~', then ~o e-dominates xb in P if ~ dominates ~b I in P. X=w = ~'. e~/fl = Xb and = --g in P.~o e-precedes Xb in P if y lea* ~o in P. v lea* in P. qgr -~ s,~t in P. y ~ qgr and u ~ ~t where the relation -(terminal equiralence) is defined as :z----pin P ifxzwEPandxyo~EP", "uris": null, "num": null, "type_str": "figure" }, "FIGREF4": { "text": "Extended definitions", "uris": null, "num": null, "type_str": "figure" }, "FIGREF5": { "text": "An example ot\" union o[ RPMs", "uris": null, "num": null, "type_str": "figure" }, "FIGREF6": { "text": "(fig. 0) :. { John liked ice-cream. Mary liked chocolate} ~t of .~imple senteuces {{John. Mary}. {ice-cream. chocolate}} set ,ff ctmjoinable pairs Fig 6: Example of a set of simple sentences Consider tile plan view of the 3-dimensional repreaentation of the union of the two simple sentences shown in fig. 7 :-Example o[ 3-dimensional structure The procedure of linearization would t~tke the foil.wing path shown by the arrows in fig. 8 :-Rxample of linearization F~dlowin K the path shown we obtain the surface siring \"John and Mary liked ice-cream and chocolate\". The set of conjoinable pairs is produced by the process of [inding equivalences. The definition of i:quivalence", "uris": null, "num": null, "type_str": "figure" }, "FIGREF7": { "text": "nil\" is ,,sed to represent the empty list. \u2022 ,in an example, a Prolog clause may have the fornt :a(X V ... Z) ir b(U v ... W) a~d c(R S ... T) where a,b & c are predicate names and R,S,...,Z may represent variables, constants or terms. (Variables are ,listinguished by capitalization of the first character in the variable name.) The intended logical read-ing of tile clause is :-\"a\" holds if \"b\" and \"c\" both hold for consistent bindings of the arguments X,Y,...,Z, U, V,..., W, R,S,...,T", "uris": null, "num": null, "type_str": "figure" }, "FIGREF8": { "text": "The device used for comparison with Dahl & McCord scheme is a simplified version of the device presented in this section. First, difference lists are used to represent strings in the following sections. For example, the pair (fig. 9) :-{ john.liked.ice-cream.Continuation. Continuation} Fig g: Example of a difference list is a difference list representation of the sentence \"John liked ice-cream\". We can :tow introduce two predicates linearize and equivaleutpalrs which correspond to the processes uf liaearization uJl(l liuding equivalences respectively (fig. 10) :linearize( pairs S1 El and 52 E2 candidates Set yivcs Sentence) Linearize hohls when a pair of difference lists ({S1. EL} & {S2. E2)) and a set ,,f candidates (Set) arc consistent with the string (Sentence)", "uris": null, "num": null, "type_str": "figure" }, "FIGREF9": { "text": "nil) using as candidate pairs for conjoining, the set o\u00a3 non-redundant pairs of equivalent terminal strings (Set).Parse holds when Sentence is the conjoined set, tence resulting from the linearization of the pair of dilference lists (S1. El) anti ($2. E2) provided that the set of candidate pairs for conjoining (Subset) is a subset of the set of pairs of equivalent terminal strings (Set).", "uris": null, "num": null, "type_str": "figure" }, "FIGREF10": { "text": "Logical readhtg for generate & parse Fig 10: Predicates llneari~.e & equivalentpairs", "uris": null, "num": null, "type_str": "figure" }, "FIGREF11": { "text": "{Alice saw Bill. Mary saw Bill} would prt.hwr the, equiwdrnt pairs :-{Alice saw Bill. Mary saw Bill} {Alice, Mary} {Alice saw. Mary saw} l\"ig. 16: l'Jxatuple of equivalent pairs Wc also make tile rollowing restriction.~ on Goodall's definition :-\u2022 If there exists two terminal strings X & Y such that X-'=xxfl & Y--xYf'/, then X &. 1\"~ should be the strongest possible left ~ right contexts respectively -provided", "uris": null, "num": null, "type_str": "figure" }, "TABREF1": { "html": null, "text": "St nil anti S2 nil candidtttes Set 9ires Sentence) Prolog dclinition for generate ~. parse The subset relation is needed for the above definition of parsing hecause it can be shown [Fong?? l that the process of linearization is more constrained (in terms of the p,.rn~issible conjoinable pairs) than the process of tinding eqnivalences.", "type_str": "table", "content": "
t t) :-
generate(Sentence from St 52)
if sctol(X.Y.nil in equivalentpairs(X Y
from SI $2) is Set)
andlinearize( pair~: parse~ Sentence 9iota9 S1 El)
if Ijnearize(pairs SI E1 avd $2 E2
candidate.~ SuhSet 9ives Sentence)
nndsctot(X.\u00a5 nil in cquivalentpairs(X Y
from S1 $2) ia Set)
Fig 1 !:
", "num": null }, "TABREF4": { "html": null, "text": ",hn .~aw the ,ltltll |.hiLt Mary .~aw and Bill gay,. a bo,,k t,, hutght~d .l.hnt .~aw the man lhat lu.;trd the wotnaH rhar lattglu'd and ~aw Bill Th,. ,,tan lh;d Mary saw and h(.ard", "type_str": "table", "content": "
Sample/ MSGRPM
encesJ system device
Each m;ul ate an apish \u00b0 ;~.lld ;t pear [662292
.Iolm at,, ~lt appl,, and a pear[ f613233
Z~k ;t,I ;Ll,ll ;1 WOIIU~.,, ~ilW o;i{'h trttill I319506
Eiit'h ll,;lll ;tllll ,'ach wl|l,llt|t at('l320503
,\"m pple
J,~hll saw and the woman heard78883'i
aa, lhat laughed
.]ohn drov,. Ihe car through and2751032
ct)m ~h.lt'ly demolishe, l a windowI
\"rh,, woa,t;tl, wit,) gav(\" a l),~ok to--10073375
.John and dr,we ;L car through .' L
window laugh~l
.h~;LVI' ,'~.ll ;).llllll\" t,I ,,;[l'h ~viHlla[~i.139 636 sot ,9~, 3It 323
.h,htl mtw a /uul Mary .~aw the red726770i!
pear
Fig. ld: Timings For some sample sentences
", "num": null } } } }