| { | |
| "paper_id": "W98-0129", | |
| "header": { | |
| "generated_with": "S2ORC 1.0.0", | |
| "date_generated": "2023-01-19T06:06:04.650629Z" | |
| }, | |
| "title": "Description Theory, LTAGs and Underspecified Semantics*", | |
| "authors": [ | |
| { | |
| "first": "Reinhard", | |
| "middle": [], | |
| "last": "Muskens", | |
| "suffix": "", | |
| "affiliation": { | |
| "laboratory": "", | |
| "institution": "Tilburg University", | |
| "location": { | |
| "postBox": "P.O. Box 90153", | |
| "postCode": "5000 LE", | |
| "settlement": "Tilburg", | |
| "country": "The Netherlands" | |
| } | |
| }, | |
| "email": "" | |
| } | |
| ], | |
| "year": "", | |
| "venue": null, | |
| "identifiers": {}, | |
| "abstract": "", | |
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| "paper_id": "W98-0129", | |
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| "abstract": [], | |
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| "text": "An attractive way to model the relation between an underspecified syntactic representation and its completions is to let the underspecified representation correspond to a logical description and the completions to the models of that description. This approach, which underlies the Description Theory of (Marcus et al. 1983) has been integrated in (Vijay-Shanker 1992} with a pure unification approach to Lexicalized Tree-Adjoining Grammars (Joshi et al. 1975 , Schabes 1990 . We generalize Description Theory by integrating semantic information, that is, we propose to tackle both syntactic and semantic underspecification using descriptions. 1 Our focus will be on underspecification of scope. We use a generalized version of LTAG, to which we shall refer as LFTAG. Although trees in LFTAG have surface strings at their leaves and are in fact very close to ordinary surface trees, there is also a strong connection with the Logical Forms (LFs) of (May 1977) . We associate logical interpretations with these LFs using a technique of intemalising the logical binding mechanism (Muskens 1996) . The net result is that we obtain a Description Theory-like grammar in which the descriptions underspecify semantics. Since everything is framed in classical logic it is easily possible to reason with these descriptions.", | |
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| { | |
| "start": 303, | |
| "end": 323, | |
| "text": "(Marcus et al. 1983)", | |
| "ref_id": "BIBREF5" | |
| }, | |
| { | |
| "start": 440, | |
| "end": 458, | |
| "text": "(Joshi et al. 1975", | |
| "ref_id": "BIBREF3" | |
| }, | |
| { | |
| "start": 459, | |
| "end": 473, | |
| "text": ", Schabes 1990", | |
| "ref_id": "BIBREF10" | |
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| "start": 948, | |
| "end": 958, | |
| "text": "(May 1977)", | |
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| "start": 1077, | |
| "end": 1091, | |
| "text": "(Muskens 1996)", | |
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| "text": "Descriptions in our theory model three kinds of information. First, there are input descriptions, which", | |
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| "section": "Syntactic Composition", | |
| "sec_num": "1" | |
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| "text": "\u2022we wish to thank Kurt Eberle, Barbara Partee, Stanley Peters and all other participants of the Bad Teinach Workshop on Models of Underspecification and the Representation of Meaning (May 1998) for their comments and criticisms on an earlier version of this paper.", | |
| "cite_spans": [ | |
| { | |
| "start": 183, | |
| "end": 193, | |
| "text": "(May 1998)", | |
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| "section": "Syntactic Composition", | |
| "sec_num": "1" | |
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| "text": "1 The approach to underspecified semantics taken in (Muskens 1995) was very much inspired by Description Theory and the work ofVijay-Shanker in (Vijay-Shanker 1992) but did not offer an actual integration with Tree-Adjoining Grammars. In this paper we endeavour to set this right.", | |
| "cite_spans": [ | |
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| "start": 52, | |
| "end": 66, | |
| "text": "(Muskens 1995)", | |
| "ref_id": "BIBREF7" | |
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| "section": "Syntactic Composition", | |
| "sec_num": "1" | |
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| "text": "Emiel Krahmer IPO Eindhoven University of Technology P.O. Box 513 5600 lvIB Eindhoven, The Netherlands krahrner\u00a9ipo.tue.nl vary per sentence. For example, for sentence (1) we have (2) as an input description. lt says that there are two lexical nodes, 2 labeled John and walks respectively; that the first of these precedes the second; and that these two lexical nodes are all that were encountered. Secondly, there is a lexicon which includes semantic information. The ent ries for John and walks are given in (3) and (4).", | |
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| "section": "Syntactic Composition", | |
| "sec_num": "1" | |
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| { | |
| "text": "(1) John walks.", | |
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| "section": "Syntactic Composition", | |
| "sec_num": "1" | |
| }, | |
| { | |
| "text": "( ", | |
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| "section": "Syntactic Composition", | |
| "sec_num": "1" | |
| }, | |
| { | |
| "text": "EQUATION", | |
| "cite_spans": [], | |
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| "eq_spans": [ | |
| { | |
| "start": 0, | |
| "end": 8, | |
| "text": "EQUATION", | |
| "ref_id": "EQREF", | |
| "raw_str": "2) 3n1n2(lex(n1)i\\lex(n2)J\\n1-< n2i\\lab{n1,john)J\\ lab(n2, waiks) A Vn(lex(n) -t (n = n1 V n = n2))) (3) \\ln 1 (lab(n1,john) -t 3n3(/ab(n3,11p)i\\n3 <ln1/\\ a+(n3) =n1 Au(n3) = John/\\ Vn{a+(n) = n1 -t (n = n3 V n = n1))/\\ Vn(a-(n) = n 1 -t n = n1)))", | |
| "eq_num": "(4" | |
| } | |
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| "section": "Syntactic Composition", | |
| "sec_num": "1" | |
| }, | |
| { | |
| "text": "= n2 -t (n = n4 V n = n1 V n = n2))J\\ a-(ns) = a-(n6) =n2A Vn(a-{n) = n2 -t (n = ns V n = 116 V n = n2))/\\ u(n4) = q(n 6 )(q(ns)) A q(n1) = >.v.wa/k v))", | |
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| "section": "Syntactic Composition", | |
| "sec_num": "1" | |
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| "text": "The function symbol a+ used in these descriptions positively anchors nodes to lexical nodes, a-negatively anchors nodes and q gives a node its semantic value. ", | |
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| "section": "Syntactic Composition", | |
| "sec_num": "1" | |
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| { | |
| "text": "/'---.... det4 11!1 ~ ~ det11 n!2 nfi Vu np1a nj9 1 1 1 1 1 every5 man20 loves12 '118", | |
| "cite_spans": [], | |
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| "section": "Syntactic Composition", | |
| "sec_num": "1" | |
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| "text": "womann Figure 1 : Elementary descriptions for every man loves a woman negative anchoring in the following way. lf a description contains the information that a certain nonlexical node is positively (negatively) anchored, the term referring to that node gets a plus (minus) sign. But pluses and minuses cancel and terms that would get a \u00b1 by the previous rule will be left unmarked. Terms marked with a plus (minus) sign are to be compared with the bottorn (top) parts of Vijay-Shanker's 'quasi-nodes' in (Vijay-Shankar 1992). There is also an obvious close connection with positive (negative) occurrences of types in complex types in Categorial Grammar.", | |
| "cite_spans": [], | |
| "ref_spans": [ | |
| { | |
| "start": 7, | |
| "end": 15, | |
| "text": "Figure 1", | |
| "ref_id": null | |
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| "sec_num": "1" | |
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| "text": "To the third and final kind of descriptions belang\u2022 a.\"'<ioms which say that <l, <l\" and -< behave like immediate dominance, dominance and precedence in trees (Al -AlO, see also e.g., Cornell 1994 , Backofen et al. 1995 3 combined with other general information, such as the statements that labeling is functional (All), and that different labe! names denote different labels (A12). Al3 and Al4 say that all nodes must be positively anchored to lexical nodes and that all lexical nodes are positively anchored to themselves. The axioms for negative anchoring (Al5 and Al6) are similar, but allow the root r to be negatively anchored to itself. 113", | |
| "cite_spans": [ | |
| { | |
| "start": 184, | |
| "end": 196, | |
| "text": "Cornell 1994", | |
| "ref_id": "BIBREF2" | |
| }, | |
| { | |
| "start": 197, | |
| "end": 219, | |
| "text": ", Backofen et al. 1995", | |
| "ref_id": "BIBREF0" | |
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| "section": "Syntactic Composition", | |
| "sec_num": "1" | |
| }, | |
| { | |
| "text": "EQUATION", | |
| "cite_spans": [], | |
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| "eq_spans": [ | |
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| "start": 0, | |
| "end": 8, | |
| "text": "EQUATION", | |
| "ref_id": "EQREF", | |
| "raw_str": "Al Vk [r <l+ k V r = kj A2 Vk\u2022k <l+ k A3 Vk 1 k2k3 [[k1 <J+ k2 /\\ k2 <J+ k3J --t ki <J+ k3} A4 Vk\u2022k-<k A5 Vk 1 k2k3 [{k1 -< k2 /\\ k2 -< k3J --t k1 -< kJ] A6 Vk 1 k2 [k1 -< k2 V k2 -< k1 V k1 <l+ k2V k2 <l+ k1 V ki = k2] A7 Vk 1 k2k3 [[k1 <l+ kz /\\ k1 -< k3] --t k2 -< k3] AB Vk 1 k2k3 [[k1 <l+ k2 /\\ k3 -< ki] --t k3 -< k2]", | |
| "eq_num": "3Note" | |
| } | |
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| "section": "Syntactic Composition", | |
| "sec_num": "1" | |
| }, | |
| { | |
| "text": "A9 Vk1k2 [k1 <l k2 --t k1 <l+ k2] AlO Vk 1 k2k3 \u2022[k1 <l k3 /\\ k1 <l+ k2 /\\ k2 <l+ k3] All vwe1 e2 {[lab(k, e1) /\\ lab(k, f2)] --t e1 = e2]", | |
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| "eq_spans": [], | |
| "section": "Syntactic Composition", | |
| "sec_num": "1" | |
| }, | |
| { | |
| "text": "Al2 1 1 ::f:. l 2 , if ! 1 and h are distinct labe! names", | |
| "cite_spans": [], | |
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| "section": "Syntactic Composition", | |
| "sec_num": "1" | |
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| { | |
| "text": "Al3 \\lk lex(a+(k)) Al4 \\lk [lex(k) -t a+(k) = k] AI5 Vk[k = rv lex(a-(k))]", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Syntactic Composition", | |
| "sec_num": "1" | |
| }, | |
| { | |
| "text": "A16 Vk [[lex(k) ", | |
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| { | |
| "start": 7, | |
| "end": 15, | |
| "text": "[[lex(k)", | |
| "ref_id": null | |
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| "section": "Syntactic Composition", | |
| "sec_num": "1" | |
| }, | |
| { | |
| "text": "V k = rJ --t a:-(k) = k]", | |
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| "section": "Syntactic Composition", | |
| "sec_num": "1" | |
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| "text": "Together with this extra information (2), (3) and (4) conspire to determine a single model. Only n1 and n 2 are lexical nodes. All nodes must be positively anchored to a lexical node. The set of nodes positively anchored to n 1 is {n 1 , n 3 } and the set positively anchored to n2 is { n 2 , n4, n1}. So the remaining n 6 and n 6 must corefer with one of the constants mentioned, the only possibility being that ns = ns and that n 6 = n1. The reader will note that in the resulting model <T(n 4 ) = walk John. The general procedure for finding out which models satisfy a given description is to identify positively marked terms with negatively marked ones in a one-to-one fashion. The term r, denoting the root, counts as negatively marked.", | |
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| "section": "Syntactic Composition", | |
| "sec_num": "1" | |
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| "text": "In the given example only one tree was described, but this is indeed an exceptional situation. lt is far more common that a multiplicity of trees satisfy a given description. This kind of underspecification enabled (Marcus et al. 1983) to define a parser which does not only work in a strict left-right fashion but is also incremental in the sense that at no point during a parse information need be destroyed. A necessary condition for this form of underspecification is that there are structures which can be described. In the context of semantic scope differences it therefore is natural to turn to (May 1977) 's Logical Forms, as. these are the kind of models required. In fact we use a variant of May's trees which is very close to ordinary surface structure: although we will allow NPs to be raised, the syntactic material of such NPs will in fact remain in situ. But while the only syntac-tic effect of raising will be the creation of an extra S node and Logical Forms will have their corresponding surface structures as subtrees, the 'movement' has an important effect on semantic interpretation. Consider example (5).", | |
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| "end": 235, | |
| "text": "(Marcus et al. 1983)", | |
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| "start": 602, | |
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| { | |
| "text": "(5) Every man loves a woman.", | |
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| "text": "We have depicted its five lexical items in fig. 1 . With two exceptions they pretty much conform to expectation. The exceptions are that each determiner comes with a pair of S nodes dominating its NP. The basic idea here is that the long-distance phenomenon of quantifying-in is treated within the domain of extended locality of a determiner. In each case the semantics of the higher S will be composed out of the semantics of the lower S and the semantics of the NP, the semantic composition rule being quantifying-in. 4 The two Ss are to be compared to the two Ss at the adjunction site of a raised NP in May's theory. There is also an obvious connection with the (single) S where 'NP-retrieval' occurs in Cooper's theory of Quantifier Storage (see Cooper 1983) .", | |
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| "text": "4", | |
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| "end": 763, | |
| "text": "Cooper 1983)", | |
| "ref_id": "BIBREF1" | |
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| { | |
| "start": 43, | |
| "end": 49, | |
| "text": "fig. 1", | |
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| "text": "lt is easily seen that in any model of the descriptions in fig. 1 ( + the input description for (5) + our a.\"<ioms) certain identities must hold: n5 = n211 n 19 = n22, n 9 = n10 1 ns = n3, and n13 = n15 are derivable. But there is a choice between two further possibilities, as it can be the case that n2 = n14 and n 15 = n 1 , or, alternatively, that n1s = ni and n 2 = n 7 \u2022 These two possibilities will correspond to the two different readings of the sentence.", | |
| "cite_spans": [], | |
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| { | |
| "start": 59, | |
| "end": 65, | |
| "text": "fig. 1", | |
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| "text": "How can we assign a semantics to the lexical descriptions in fig. l ? We must e.g. be able to express the semantics of n 1 in terms of the semantics of n2, whatever the latter turns out to be, i.e. we must be able to express the result of quantification into an arbitrary context. In mathematical English we can say that, for any <p, the value of Vx<p is the set of assignments a such that for all b differing from a at most in x, b is an element of the value of <p. We need to be able to say something similar in our logical language, i.e. we must be able to talk about things that function like variables and constants, things that function like assignments, etc. The first will be called registers, the second states. Two primitive types are added to the logic: -rr and s, for registers and states respectively. We shall have variable registers, which stand proxy for variables and constant registers for constants. However, since registers are simply objects in our models, both variable registers and const ant registers can be denoted with variables as well as with constants. Here are some a.xioms: Each node is assigned a fresh register (A19). Constant registers have a fixed value (A20). For more information on a strongly related set of axioms see (Muskens 1996) .", | |
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| "sec_num": "2" | |
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| "text": "EQUATION", | |
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| "raw_str": "A17 Vi 5 Vvrr'<1Xe {V AR(v) 4 3j 5 {i(v]j /\\ V(v)(j) = x]] Al8 Vk V AR(u(k)) Al9 Vk 1 k2 [u(k1) = 1.1(k2) 4 ki = k2] A20 Vi.V(John\")(i) =johne, Vi.V", | |
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| "sec_num": "2" | |
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| "text": "These axioms essentially allow our logical language to speak about binding and we can now use this expressivity to embed predicate logic into (the first-order part of) type theory, with the side-effect that binding can take place on the level of registers. Write", | |
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| "text": "Ro1 . . . on for Ai.R(V(o1)(i), ... , V(c5n)(i)), not <p for Ai..,cp(i), <p & ' t/J for Ai[cp(i) /\\ tjJ(i)], cp =* ' t/J for Ai[ep(i) 4 't/J(i)], some o <p for Ai3j[i[o]j /\\ cp(j)],", | |
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| { | |
| "text": "all 0 cp for AiVj[i(o]j 4 cp(j}].", | |
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| "text": "We have essentially mimicked the Tarski truth conditions for predicate logic in our object language and in fact it can be proved that, under certain conditions,5 we can reason with terms generated in this way as if they were the predicate logical formulas they stand proxy for (see Muskens 1998) .", | |
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| "text": "lt should be stressed that the technique discussed here can be used to embed any logic with a decent interpretation into classical logic. For example, (Muskens 1996) shows that we can use the same mechanism to embed Discourse Representation Theory (Kamp & Reyle 1993) into classical logic. In a fuller version of this paper we shall also present a version of LFTAG based on Discourse P . . . eprescntations. \u2022 5 The relevant condition is that in each term IP we are using in this way, and each pair u(n), u(n') occurring in r.p, with n and n' syntactically different, we must be justified to assume n :f' n'. In the application discussed below this condition is met automatically. fig. 1 . u(n3) = Uns u(n1) = all Un 5 [u(n6)(un 5 ) => u(n2)) u(n10) = >.v.v loves u(n13) u(n1) = u(n9 )(u(ns)) a(n 16 ) = Unu u(n14) = some Un 18 [a(n19)(un 18 ) ", | |
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| "text": ">.v.v loves u(n13)", | |
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| }, | |
| { | |
| "text": "& a(n15)] u(n2il = >.v.man v u(n22) = >.v.woman v", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Internalising Binding", | |
| "sec_num": "2" | |
| }, | |
| { | |
| "text": "The first two equations derive from the lexical item for every, the third and fourth from loves, the fifth and sixth from a, and the last two from the common nouns. Note that in the translation of every, n 3 only gets a referent as its translation (namely u(n 5 ), which for readability we write as tln 5 ), while the real action is taking place upstairs. A similar remark holds for the other determiner.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Internalising Binding", | |
| "sec_num": "2" | |
| }, | |
| { | |
| "text": "As we have seen earlier, in any model of the relevant descriptions ns = n21, nrn = n22, n 9 = n 10 , Note that this is the point where we have made essential use of our internaHsation of binding: had we used ordinary variables instead of our registerdenoting terms, the substitution would not have been possible. Continuing our reasoning, we see that \u00b5nder the given assumption the root node r (=n 14 in this 115 case) will be assigned the 3V reading of the sentence. Without assumptions the disjunction in fig. 2 is derivable.", | |
| "cite_spans": [], | |
| "ref_spans": [ | |
| { | |
| "start": 507, | |
| "end": 514, | |
| "text": "fig. 2", | |
| "ref_id": null | |
| } | |
| ], | |
| "eq_spans": [], | |
| "section": "Internalising Binding", | |
| "sec_num": "2" | |
| }, | |
| { | |
| "text": "na =", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Internalising Binding", | |
| "sec_num": "2" | |
| }, | |
| { | |
| "text": "We conclude that the leading idea behind Marcus' Description Theory allows us to underspecify semantic information much in the same way as syntactic information is underspecified in this theory. The price is that we must accept that different semantic readings correspond to different structures, as the method only allows underspecification of the latter.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Internalising Binding", | |
| "sec_num": "2" | |
| }, | |
| { | |
| "text": "With lexical nodes we mean those leaves in a tree which carry a lexeme.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "In this paper only quantification into S is considered but in a fuller version we shall generalise this to qua~tification into arbitrary phrasal categories.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "", | |
| "sec_num": null | |
| } | |
| ], | |
| "back_matter": [], | |
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| "ref_entries": { | |
| "FIGREF0": { | |
| "uris": null, | |
| "text": "Mary)(i ) = mary, ... Here V AR is a predicate which singles out variable registers, V assigns a value to each register v in each state j, and i(o]j is an abbreviation of Vw[w -::/: o 4 \\!(w)(i) = V(w)(j)]. Al 7 forces states to behave like assignment.s in an essential way. The function u assigns variable registers to nodes (A18).", | |
| "num": null, | |
| "type_str": "figure" | |
| }, | |
| "TABREF2": { | |
| "html": null, | |
| "content": "<table/>", | |
| "text": "that .A9 and .AlO in themselves do not suffice to exclude that some nodes are connected by a dominance relation without there bcing a (finite) path of immediate dominances between them. In fact the nature or our input descriptions and the form of our lexicon exclude this.", | |
| "num": null, | |
| "type_str": "table" | |
| }, | |
| "TABREF3": { | |
| "html": null, | |
| "content": "<table><tr><td>Figure 2: A Derivable Disjunction</td></tr><tr><td>3 Semantic Composition</td></tr><tr><td>\\Ve can now integrate semantic equations with the</td></tr><tr><td>lexical items occurring in</td></tr></table>", | |
| "text": "u(r) = all Un 5 (man Un 5 => sorne ~n 18 [woman Unis & Uns loves Un 18 ]JV u(r) = sorne Un 18 [ woman Un 1 s & all Uns [man Un 5 => Uns loves Un 1 sJJ", | |
| "num": null, | |
| "type_str": "table" | |
| }, | |
| "TABREF4": { | |
| "html": null, | |
| "content": "<table><tr><td colspan=\"2\">a(n1) = Uns loves Un 1 s</td></tr><tr><td colspan=\"2\">u(n1) = alluns[manun 5 =>cr(n2))</td></tr><tr><td><7(n14)</td><td>= some Un 1 s [ woman tln 18 & cr(n1s)}</td></tr></table>", | |
| "text": "n3, and n13 = nl6 hold. From this it follows that The relevant constraints further imply that either nz = n14 and n1s = n1, or, alternatively, that n 15 = n1 and n2 = n7. For the moment Jet us assurne the second possibility. Since Uns loves Un 18 is a c/osed term (u is a function constant and ns and n 18 are constants that witness existential quantifiers in the input description of (5)), the assumption that n2 = n 7 allows us to conclude that cr(ni) = all Un 5 [man Uns => Un 5 loves tln 18 ]", | |
| "num": null, | |
| "type_str": "table" | |
| } | |
| } | |
| } | |
| } |