| { | |
| "paper_id": "W98-0133", | |
| "header": { | |
| "generated_with": "S2ORC 1.0.0", | |
| "date_generated": "2023-01-19T06:04:23.323210Z" | |
| }, | |
| "title": "Constructive models of extraction parameters 1", | |
| "authors": [ | |
| { | |
| "first": "Dick", | |
| "middle": [], | |
| "last": "Oehrle", | |
| "suffix": "", | |
| "affiliation": { | |
| "laboratory": "", | |
| "institution": "University of Arizona", | |
| "location": {} | |
| }, | |
| "email": "" | |
| } | |
| ], | |
| "year": "", | |
| "venue": null, | |
| "identifiers": {}, | |
| "abstract": "An important and central insight of Tree Adjoining Grammar is its factorization of local dependencies-handled through local INITIAL TREES-and recursion-handled through AUXILIARY TREES and successive applications of the ADJUNCTION operation. Many different frameworks of grammatical description have converged on a conceptually similar distinction. In the transformational tradition, the idea of long-distance movement-movement across an 'essential variable'-has been abandoned in favor of sequences of short-distance hops (or checks). In feature-based phrase structure grarnmars such as GPSG and HPSG, the analog of recursive movement is the transitive closure of local consistency conditions on local trees containing the SLASH feature. At first glance, then, this convergence in a variety of theoretical approaches suggests that recursion in some form is the essential engine in the characterization of natural language longdistance dependencies. And this assumption might lead us to the following thesis concerning the relation between recursion and extraction. Thesis: if r[a] is a well-formed expression of category A containing a gap a of category B and ~[\u00df] is a well-formed expression of category B containing a gap \u00df of category C, then the result of replacing the gap a in r(a] with .6. [\u00df], which we write", | |
| "pdf_parse": { | |
| "paper_id": "W98-0133", | |
| "_pdf_hash": "", | |
| "abstract": [ | |
| { | |
| "text": "An important and central insight of Tree Adjoining Grammar is its factorization of local dependencies-handled through local INITIAL TREES-and recursion-handled through AUXILIARY TREES and successive applications of the ADJUNCTION operation. Many different frameworks of grammatical description have converged on a conceptually similar distinction. In the transformational tradition, the idea of long-distance movement-movement across an 'essential variable'-has been abandoned in favor of sequences of short-distance hops (or checks). In feature-based phrase structure grarnmars such as GPSG and HPSG, the analog of recursive movement is the transitive closure of local consistency conditions on local trees containing the SLASH feature. At first glance, then, this convergence in a variety of theoretical approaches suggests that recursion in some form is the essential engine in the characterization of natural language longdistance dependencies. And this assumption might lead us to the following thesis concerning the relation between recursion and extraction. Thesis: if r[a] is a well-formed expression of category A containing a gap a of category B and ~[\u00df] is a well-formed expression of category B containing a gap \u00df of category C, then the result of replacing the gap a in r(a] with .6. [\u00df], which we write", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Abstract", | |
| "sec_num": null | |
| } | |
| ], | |
| "body_text": [ | |
| { | |
| "text": "As an example of a case which might be adduced in support of this thesis, consider the unbounded nature of extraction from noun phrases, as discussed by Kroch [6] . The well-formedness of Which painting did you see? indicates that did you see is a well-formed expression containing a gap of type np, and the well-formedness of Which painting did you see a photograph of? and Which painting did you see a copy of? suggests (in a way consistent with the thesis) that a photograph of and a copy of are well-formed np's containing np gaps. Accordingly, the thesis, if correct, requires that Which painting did you see a copy of a photograph of? also be well-formed, as indeed it is. Yet this simple and elegant thesis concerning recursion encounters well-known difficulties, which", | |
| "cite_spans": [ | |
| { | |
| "start": 153, | |
| "end": 162, | |
| "text": "Kroch [6]", | |
| "ref_id": null | |
| } | |
| ], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "f[.6.f,tJ]] is a well-formed expression of category A containing a gap \u00df of category C.", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "\u2022 1 This paper is the product of joint work with Michael :tvfoortgat, with whom a more comprehensive treatment of these questions is under preparation. This work has been supported by the National Science Foundation under Grant No. SBR-9510706, which we gratefully acknowledge.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "f[.6.f,tJ]] is a well-formed expression of category A containing a gap \u00df of category C.", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "have been construed as supporting additional theoretical devices such as filters and other forms of surface constraints. The goal of this paper is to show in the most direct possible way that in one well-known case, it is possible to formulate recursive principles in a way that obviates the need for additional theoretical mechanisms and, at the same time, offers a simple formal characterization of a proposed typological distinction of long-standing interest.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "f[.6.f,tJ]] is a well-formed expression of category A containing a gap \u00df of category C.", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "As Perlmutter [15, 16] first observed, extraction from the np-position following a complementizer js possible in some languages, but not in others. Tlms There are two basic strategies to deal with these issues. The first is to propose general grammatical rules (selectively chosen by each language) which generate exactly the grammatical examples and fail to generate the ungrammatical examples; the second is to propose general grammatical principles which generate all the good examples and couple these principles wih constraints (selectively chosen by each language) which weed out particular cases. We call the first strategy 'constructive' and the second 'co-constructive'. There have been rnany co-constructive proposals to account for the above phenomena: we rnention here only [15, 16, 1, 2] . In the sections to follow, we develop simple and appealingly syrnmetrical constructive accounts of these constrasting systems of extraction.", | |
| "cite_spans": [ | |
| { | |
| "start": 14, | |
| "end": 18, | |
| "text": "[15,", | |
| "ref_id": "BIBREF14" | |
| }, | |
| { | |
| "start": 19, | |
| "end": 22, | |
| "text": "16]", | |
| "ref_id": "BIBREF15" | |
| }, | |
| { | |
| "start": 148, | |
| "end": 152, | |
| "text": "Tlms", | |
| "ref_id": null | |
| }, | |
| { | |
| "start": 786, | |
| "end": 790, | |
| "text": "[15,", | |
| "ref_id": "BIBREF14" | |
| }, | |
| { | |
| "start": 791, | |
| "end": 794, | |
| "text": "16,", | |
| "ref_id": "BIBREF15" | |
| }, | |
| { | |
| "start": 795, | |
| "end": 797, | |
| "text": "1,", | |
| "ref_id": "BIBREF0" | |
| }, | |
| { | |
| "start": 798, | |
| "end": 800, | |
| "text": "2]", | |
| "ref_id": null | |
| } | |
| ], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "A typological pammeter", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "We work in the framework of multi-modal grammatical logic [10, 11, 4, 9, 14, 12] , a framework we describe here only in enough depth to support the goals of this paper. F'rom this perspective, the problem of grammatical cornposition, within and across such different dimensions of linguistic structure, is regarded as an inference problem: the component pieces of a complex linguistic structure are taken tobe the premisses of a deductive problem, and its global structure to be a conclusion deducible from these premisses in a system of grammatical inference. Thus, grammaticality is identified with validity within this system. Moreover, the formal system characterizing validity offers a natural model, in the style of denotational semantics for programming languages [17J, of the cognitive computation that must be assumed to provide the basis for real-time understanding of i;unning speech. 2 Thus the logical methods described here are not introduced in a blind search for formal rigor; on the contrary, they are introduced because they provide an armentarium of subtle and suitable tools and methods tliat allow us to probe the properties of grammatical reasoning.", | |
| "cite_spans": [ | |
| { | |
| "start": 58, | |
| "end": 62, | |
| "text": "[10,", | |
| "ref_id": "BIBREF9" | |
| }, | |
| { | |
| "start": 63, | |
| "end": 66, | |
| "text": "11,", | |
| "ref_id": "BIBREF10" | |
| }, | |
| { | |
| "start": 67, | |
| "end": 69, | |
| "text": "4,", | |
| "ref_id": "BIBREF3" | |
| }, | |
| { | |
| "start": 70, | |
| "end": 72, | |
| "text": "9,", | |
| "ref_id": "BIBREF8" | |
| }, | |
| { | |
| "start": 73, | |
| "end": 76, | |
| "text": "14,", | |
| "ref_id": "BIBREF13" | |
| }, | |
| { | |
| "start": 77, | |
| "end": 80, | |
| "text": "12]", | |
| "ref_id": "BIBREF11" | |
| }, | |
| { | |
| "start": 896, | |
| "end": 897, | |
| "text": "2", | |
| "ref_id": null | |
| } | |
| ], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "The fmmework", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "In such a system, if A is deducible from a structured set of premisses r, we write r :::::> A. lt is reasonable to suppose that the deducibility relation is reflexive and transitive: that is, for every formula A, we have A :::::> A; and for every triple of formulas A, B, C, if A::::} B and B::::} C , then A::::}C.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "The fmmework", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "A uni-modal deductive system contains a single way (or mode) of putting resources premisses together. To reason about this mode, we introduce a product operator-a form of conjunctiontogether with its residuals (or adjoints)-forms of implication. For example, given a binary mode of composition, we have a product \u2022 and two directionally-sensitive implications written, as in the categorial tradition, / and \\. Every product and its adjoints are connected by the basic adjointness laws. In the binary case, as here, these take the form:", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "The fmmework", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "A :::::> C / B iff A \u2022 B ::::} C iff B ::::} A \\ C", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "The fmmework", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "As a simple illustration of the consequences of the adjointness Iaws, take A to be C / B; by reftexivity, we have C / B ::::} C / B; using the first adjointness law (left to right), we have ( C / B) \u2022 B :::::> C. This is called the co-unit of the adjunction and is also known variously as Modus Ponens (in the logical literature) or (functional) application (in the categorial literature).", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "The fmmework", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "There are a number of different presentations of this system of pure binary residuation logic: Gentzen style, natural deduction, Hilbert-style, proof nets. These can be easily shown to be equivalent with regard to provability and we identify them all with the non-associative Lambek calculus NL [7] .", | |
| "cite_spans": [ | |
| { | |
| "start": 295, | |
| "end": 298, | |
| "text": "[7]", | |
| "ref_id": "BIBREF6" | |
| } | |
| ], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "The fmmework", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "Keeping the logical rules expressed by the adjointness laws invariant, we may obtain other logical systems by adding structural rules [3, 5) , such as the following:", | |
| "cite_spans": [ | |
| { | |
| "start": 134, | |
| "end": 137, | |
| "text": "[3,", | |
| "ref_id": "BIBREF2" | |
| }, | |
| { | |
| "start": 138, | |
| "end": 140, | |
| "text": "5)", | |
| "ref_id": "BIBREF4" | |
| } | |
| ], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "The fmmework", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "RAssoc (A \u2022 B) \u2022 C::::} A \u2022 (B \u2022 C) LAssoc A \u2022 (B \u2022 C)::::} (A \u2022 B) \u2022 C Perm A \u2022 B :::::> B \u2022 A Contr A::::} A\u2022 A RWeak A\u2022B::::} A LWeak A\u2022B => B '2", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "The fmmework", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "Analogously, we may think of models of the unfolding processes of speech comprehension at the psychological and neurological levels as approximat.ions, at different levels of scale, of the operational semantics of this process.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "The fmmework", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "The presence or absence of these rules defines a family of unimodal logics of conjunction and implication, some of whose members (with characteristic arrows) are:", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "The fmmework", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "logic structural rules arrows NL none (A/B) \u2022 B => A, B => (A/B)\\B L RAssoc, LAssoc LP RAssoc,LAssoc,Perm A/B => (A/C)/(B/C), A\\(B/C) => (A\\B)/C A/B => B\\A, (A/B)/C => (A/B)/C)", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "The fmmework", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "When a particular formuia is provable in a particular logical system, we indicate this using Frege's symbol f-. Tims,", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "The fmmework", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "NL f-s/(np\\s) \u2022 (s/(np\\s)\\s) => s L f-vp/np => (vp/pp)/(np/pp)", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "The fmmework", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "If a formula is not provable in a particular system, we draw a slash through the turnstile, as in", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "The fmmework", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "NL lf vp/np => (vp/pp)/(np/pp)", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "The fmmework", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "From this general perspective, then, binary unimodal deductive systems are definable simply by specifying, once and for all, what structural rules the single mode of composition enjoys.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "The fmmework", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "Although the applicability of these systems to the analysis of natural language properties has been the subject of intense scrutiny, it is clear that natural languages differ from unimodal deductive systems in au essential way. Namely, they exhibit a much more subtle control of inference than the all or nothing choice of structural rules allows. For example, individual languages often exhibit varying sensitivity to order. Japanese and Korean, for example, are strict about the position of the tensed verb in a clause but not strict about the position of the arguments preceding the verb. This suggests a richer deductive system, one based on multiple modes of combination. 3 Each mode has a fixed arity, an associated product operator of that arity and an irnplication for each argument position, satisfying the adjointness laws. Each mode is associated with a set of structural rules. However, something new arises as weil: structural postulates involving more than one mode.", | |
| "cite_spans": [ | |
| { | |
| "start": 677, | |
| "end": 678, | |
| "text": "3", | |
| "ref_id": "BIBREF2" | |
| } | |
| ], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "The fmmework", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "As an illustration which will be important in the sequel, consider a systern with a single binary mode, associated with the binary product \u2022 and adjoints / and \\, and a single unary mode, associated with a unary operator 0 and a single adjoint ol. The adjointness laws for the unary operator take the form:", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "The fmmework", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "OA => B iff A => o!\u00df", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "The fmmework", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "Just as we derived the co-unit above by starting with the sequent C/B::::} C/B, if take A above to be ol B, then the right hand side holds by reftexivity and the left hand side gives us a unary counterpart to Modus Ponens: 4 oolA::::} A In other words, if the unary operator <> has an adjoint, then the composition of oo! has an interesting property: it can play a role in part of a deduction and then disappear. This property is the first of two crucial properties of multi-modal type logic we will need below. The second, a small set of structural rules involving the interaction of <> and \u2022, will be developed below, after we prepare the ground by developing some very small fragments which will support the illustration of the extraction parameters of interest here.", | |
| "cite_spans": [ | |
| { | |
| "start": 223, | |
| "end": 224, | |
| "text": "4", | |
| "ref_id": "BIBREF3" | |
| } | |
| ], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "The fmmework", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "We now develop the simplest possible fragments of French, English, and Dutch without extraction which can be directly extended to support the extraction constructions of interest. The many points of grarnrnatical interest that these fragments tauch on that are not directly relevant to the problem at hand will be systematically ignored. The logical framework is simply the pure residuation logic NL: \u2022, /, and \\ connected by the adjointness laws; no added structural rules. From this point of view, all that remains tobe added is a set of atomic formulas (categories), common to all the fragments, and a set of lexical assumptions associating basic expressions with formulas. 4 0ne may connect t.his straightforwardly with the binary case discussed earlier by regarding the product A \u2022 B as t.he result of applying the unary operator A \u2022to B. This unary operator may be regarded as a modalit.y OA, whose corresponding adjoint o1 is the unary operator A\\which yields A\\B when applied to B. These fragments arc of course extremely simple. This is obvious at the lexical level, since each fragment contains fewer than 10 words and speakers of natural languages are estimated to know 6 Actually, we let t stand for a generalization of transitivity which is easily shown to be valid in the presence of the adjointness laws. We illustrate with a simple special case. Suppose", | |
| "cite_spans": [ | |
| { | |
| "start": 677, | |
| "end": 678, | |
| "text": "4", | |
| "ref_id": "BIBREF3" | |
| }, | |
| { | |
| "start": 1181, | |
| "end": 1182, | |
| "text": "6", | |
| "ref_id": "BIBREF5" | |
| } | |
| ], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Fragments without extraction", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "A => B and C \u2022 B => D. By adjointness, C \u2022 B => D ijf B => C\\D", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Fragments without extraction", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "By our second premise, the lefthand side holds; thus, the righthand side holds; by our first premise and transitivity, we have A => C\\D; taking this as the righthand side of the adjointness Jaw, the lefthand side gives us", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Fragments without extraction", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "C \u2022 A => D.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Fragments without extraction", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "Tims, WC' have proved the derived rule of inference (with premisses represented on top of the line and conclusion below):", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Fragments without extraction", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "A=>B C\u2022B=>D C\u2022A~D", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Fragments without extraction", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "By an easy inductive argument, this simple result can be generalized to show that. we can generalize transitivity to substit ution inside a product of arbitrary depth.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Fragments without extraction", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "on the order of tens of thousands of words. This can be remedied in part by enriching the lexicon. But enriching the lexicon is not in and of itself a sufficient remedy.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Fragments without extraction", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "In the next section, we will examine the well-known inadequacies of NL as a logic of extraction and show how simple extensions of it can accommodate the properties of interest here of languages like French, English, and Dutch.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Fragments without extraction", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "An embedded question, such as qui a vu Martin in a French sentence such as Jean s'est demande qui a vu Martin or who saw Martin in an English sentence like Jean wondered who saw Martin, consists of two basic parts: the question word who and the body---the clausal remnant saw Martin. Although the system NL is too weak to deal adequately with French or English embedded questions, its type system can handle this particular case and shows the way toward a system that handles a much \u2022 'broader range of cases.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Extraction: preliminaries", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "We begin with the following fact, which follows directly from the lexical properties of the words in question by the adjointness laws:", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Extraction: preliminaries", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "NL, *ngl*sh f-saw \u2022 Martin => np\\s Now, writing cq for the type of an embedded question, adjointness allows us to solve for the unknown type :r in the sequent", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Extraction: preliminaries", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "(x \u2022 (np\\s)) => cq iff x => cq/(np\\s)", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Extraction: preliminaries", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "Thus, adding cq to our stock of atoms and extending our lexical assignment by the declaration who :::::> cq/(np\\s), we can prove:", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Extraction: preliminaries", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "Jean \u2022 (wondered \u2022 (who \u2022 (saw \u2022 Martin)))=> s", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Extraction: preliminaries", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "This analysis is lexically extendable to embedded questions with complementizer whether, by the addition of the lexical type declaration whether => cq / s But further generalizations within the system NL are only possible if completely unacceptable forms of lexical polymorphism are allowed. For example, to treat the embedded question who Martin saw from this perspective, we would need tobe able to assign a type to Martin saw, which requires a new t.ype np\\(s/np) for saw, relative to which we can show Martin \u2022 saw => s/np. But we also need a new type for who, cq/(s/np), in order tobe able to derive who Martin saw as a cq. Switching the basic inference system from NL to L by adding the two Associativity rules allows one to combine all the cases in which the gap is rightmost into a single category (since it is possible to show that in the presence of Associativity that all clausal remnants with a single, final np gap belong to the type s/np), but distinct types are still needed for intial and final gaps and non-peripheral cases still rernain.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Extraction: preliminaries", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "Before proceeding further, it is worthwhile to take stock of the situation. We seek a system of inference with the following properties:", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Extraction: preliminaries", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "1. there is a type e such that we may take who, for exarnple, tobe of type cq/(e\\s) and we may . show using hypothetical reasoning, that the body is provably of type e\\s; All these desiderata can be simultaneously satisfied in a simple multi-modal system of grammatical inference.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Extraction: preliminaries", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "Ext.end NL by the addition of a unary mode associated with the unary type constructor <>wh and its adjoint ot,h, to form the system we shall refer to as NLowh. Recall that by the adjointness laws, we have Now, if we assume that the single type assignment in our fragment for who is then we can treat who saw Martin as an embedded question, since we have Tlms, for the special case in which the body of the embedded question is of type np\\s, we now have two types for who which satisfy all our desiderata (some vacuously), namely the NL-type cq/(np\\s) and the NLowh-t.ype cq/(<>w1tD~hnp\\s). We have already seen that the first of these is difficult to ext.end uniformly to a larger range of relevant cases, for at least two reasons:", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Extraction: a multi-modal approach", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "\u2022 atomic categories like np are not part of the logical vocabulary, so our logical system cannot formulate general laws in terms of particular atoms;", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Extraction: a multi-modal approach", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "\u2022 on the other side of the coin, formulating filler-gap communication in terms of particular atoms would miss the point, since similar communication rules hold with respect to other atomic categories (such as ap and pp).", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Extraction: a multi-modal approach", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "In fact, in standard generative syntax, these problems were recognized very early, and movement rules were formulated not with regard to partictilar categories, but with regard to a particular feature (or set of features), such as [+wh] . But in contrast to the inert feature [+wh] , which has no intrinsic logical behavior, the type constructor <>wh is a logical operator, with an adjoint D~h\u2022 But over and above the behavior of the Operator <>wh with its adjoint D~h (which plays a role in the proof displayed above), as a product operator, <>wh can also appear in interaction rules, connecting it with other operators.", | |
| "cite_spans": [ | |
| { | |
| "start": 231, | |
| "end": 236, | |
| "text": "[+wh]", | |
| "ref_id": null | |
| }, | |
| { | |
| "start": 276, | |
| "end": 281, | |
| "text": "[+wh]", | |
| "ref_id": null | |
| } | |
| ], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Extraction: a multi-modal approach", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "We have already seen how the type cq/( oo!np\\s) accounts for French, English, and Dutch sentences such as:", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Extraction: a multi-modal approach", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "Unlike K 2l, the postulate K2r is not recursive, since its output can never be matched to its input. Still, in English, the output of K2r must be able to communicate with more deeply embedded positions, as in Jean wondered (who (Maxima (tried (to (telephone))))) Jean wondered (who (Maxima (persuaded (to (telephone Kirn)))))", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Extraction: a multi-modal approach", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "These examples are obtainable with the mirror images of the postulates for Dutch:", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Extraction: a multi-modal approach", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "-- K lr ((A \u2022 B) \u2022 <>C) => ((A \u2022 <>C) \u2022 B) -- K 2r ((A \u2022 B) \u2022 <>C) => (A \u2022 (B \u2022 <>C))", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Extraction: a multi-modal approach", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "We assume that these postulates hold for French as well as English. On this view then, the differences between French and English, on the one hand, and Dutch, on the other, reside in the choice between two sets of interaction postulates, displayed in Figures 1 and 2 . The Out.eh postulates allow an extracted phrase to occur directly following a complementizer. For example, consider the sentence Wie zei Marie dat die appel opgegeten heeft? Figure 3 displays the bracketing we assume and the succession of structures involved in a proof. 8 On the other hand, the postulates proposed here for English and French do not allow extract1on sites to follow a complementizer. More precisely, although it is possible for a modally-decorated expression to communicate with the position following a complementizer, this requires the expression to be on the right. branch of a binary structure lVhosc lcft brar~ch is the cornplementizer 1 and this position makes it impossible for the expression to combine with the predicate.", | |
| "cite_spans": [ | |
| { | |
| "start": 540, | |
| "end": 541, | |
| "text": "8", | |
| "ref_id": "BIBREF7" | |
| } | |
| ], | |
| "ref_spans": [ | |
| { | |
| "start": 251, | |
| "end": 266, | |
| "text": "Figures 1 and 2", | |
| "ref_id": "FIGREF2" | |
| }, | |
| { | |
| "start": 443, | |
| "end": 451, | |
| "text": "Figure 3", | |
| "ref_id": null | |
| } | |
| ], | |
| "eq_spans": [], | |
| "section": "Extraction: a multi-modal approach", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "((zei Marie) (dat (<>Dlnp ((die appel) (opgegeten heeft))))) __, ((zei Marie)(<>o!np (dat ((die appel) (opgegeten heeft))))) !f 2 [ oo!np((zei Marie)(dat ((die appel) (opgegeten heeft)))) J( 2 l The principles of distributivity on which the above account of extraction systems depends on are non-deterministic and dynamic. These properties distinguish this approach from alternatives in the literature and offer new perspectives on natural language extraction systems. The fuller report on this research in preparation will contain a comparison with current theoretical alternatives mentioned in the introduction.", | |
| "cite_spans": [ | |
| { | |
| "start": 128, | |
| "end": 131, | |
| "text": "2 [", | |
| "ref_id": null | |
| } | |
| ], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Discussion", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "In fact. the presence of .more than one mode of combination is implicit in linguistic practice: phonologists and morphologists have recognized different kinds of boundaries between elements; X-bar theory recognizes different modes of combination ('spec-head' relation, for example) at different levels.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "The presence of asterisks is to emphasize the fragmentary character of these simple grammatical systems.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "F\\1ll details of the proof depend on an analysis of extraposition, which we need not pursue here.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "", | |
| "sec_num": null | |
| } | |
| ], | |
| "back_matter": [ | |
| { | |
| "text": "French Jean se demandait qui a vu Martin.Jean reft asked:impf who has seen Martin 'Jean was wondering who saw :rviartin.'English Jean was wondering who saw Martin.", | |
| "cite_spans": [], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "annex", | |
| "sec_num": null | |
| }, | |
| { | |
| "text": "Jan vroeg zieh af wie slaapte Jan asked refi who slept 'Jan wondered who slept.'The next simplest step of communication between filler and gap involves sentences such as:French In French and English, these sentences will be derivable if we add the following interaction postulate:In Dutch, the required interaction postulate is:These postulates are pleasantly symmetric. To see that they do what we say they do, look at the proofs below: \\Vhile J( 21 allows the modally-decorated type to look recursively down the left branch of a right brauch, it is also possible in Dutch to find the gap down the left branch of a left branch: 7 Jan vroeg zieh af ((op wie)(Marie (gestellt was))) Jan asked refi particle prep whom Marie like \u2022Jan wondered who l\\farie liked' In this example, the extracted pbrase must communicate with the position to the left of gestellt. This is accomplished by adding to the Dutch postulate pack.age the interaction postulate K ll, formulated below: 7 Thc example involves pied-piping with the preposition op; this fact is orthogonal to our interests here, so is not pursued here. For treatments of pied-piping, see Morrill {13] .", | |
| "cite_spans": [ | |
| { | |
| "start": 629, | |
| "end": 630, | |
| "text": "7", | |
| "ref_id": "BIBREF6" | |
| }, | |
| { | |
| "start": 971, | |
| "end": 972, | |
| "text": "7", | |
| "ref_id": "BIBREF6" | |
| }, | |
| { | |
| "start": 1137, | |
| "end": 1149, | |
| "text": "Morrill {13]", | |
| "ref_id": null | |
| } | |
| ], | |
| "ref_spans": [], | |
| "eq_spans": [], | |
| "section": "Dutch", | |
| "sec_num": null | |
| } | |
| ], | |
| "bib_entries": { | |
| "BIBREF0": { | |
| "ref_id": "b0", | |
| "title": "Theory of Complementation in English Syntax", | |
| "authors": [ | |
| { | |
| "first": "J", | |
| "middle": [ | |
| "W" | |
| ], | |
| "last": "Bresnan", | |
| "suffix": "" | |
| } | |
| ], | |
| "year": 1972, | |
| "venue": "", | |
| "volume": "", | |
| "issue": "", | |
| "pages": "", | |
| "other_ids": {}, | |
| "num": null, | |
| "urls": [], | |
| "raw_text": "J.W. Bresnan. 1972. Theory of Complementation in English Syntax. Ph.D. dissertation. MIT.", | |
| "links": null | |
| }, | |
| "BIBREF2": { | |
| "ref_id": "b2", | |
| "title": "The Collected Papers of Gerhard Gentzen", | |
| "authors": [ | |
| { | |
| "first": "G", | |
| "middle": [], | |
| "last": "Gentzen", | |
| "suffix": "" | |
| } | |
| ], | |
| "year": null, | |
| "venue": "Untersuchungen \u00fcber das logische Schliessen", | |
| "volume": "39", | |
| "issue": "", | |
| "pages": "1934--1939", | |
| "other_ids": {}, | |
| "num": null, | |
| "urls": [], | |
| "raw_text": "G. Gentzen. 1934-5. Untersuchungen \u00fcber das logische Schliessen, Mathematische Zeitschrift 39, pp. 176-210. 405-431. (English translation in M. E. Szabo, ed., The Collected Papers of Gerhard Gentzen, North-Holland 1 Amsterdam).", | |
| "links": null | |
| }, | |
| "BIBREF3": { | |
| "ref_id": "b3", | |
| "title": "Comparatives and Categorial Grammar", | |
| "authors": [ | |
| { | |
| "first": "P", | |
| "middle": [], | |
| "last": "Hendriks", | |
| "suffix": "" | |
| } | |
| ], | |
| "year": 1995, | |
| "venue": "", | |
| "volume": "", | |
| "issue": "", | |
| "pages": "", | |
| "other_ids": {}, | |
| "num": null, | |
| "urls": [], | |
| "raw_text": "P. Hendriks. 1995. Comparatives and Categorial Grammar. Ph.D. dissertation. Rijksuniver- siteit Groningen.", | |
| "links": null | |
| }, | |
| "BIBREF4": { | |
| "ref_id": "b4", | |
| "title": "Introduction to Metamathematics. D. Van Nostrand", | |
| "authors": [ | |
| { | |
| "first": "S", | |
| "middle": [ | |
| "C" | |
| ], | |
| "last": "Kleene", | |
| "suffix": "" | |
| } | |
| ], | |
| "year": 1952, | |
| "venue": "", | |
| "volume": "", | |
| "issue": "", | |
| "pages": "", | |
| "other_ids": {}, | |
| "num": null, | |
| "urls": [], | |
| "raw_text": "S. C. Kleene. 1952. Introduction to Metamathematics. D. Van Nostrand, New York.", | |
| "links": null | |
| }, | |
| "BIBREF5": { | |
| "ref_id": "b5", | |
| "title": "Alternative Conceptions of Phrase Structure", | |
| "authors": [ | |
| { | |
| "first": "A", | |
| "middle": [ | |
| "S" | |
| ], | |
| "last": "Kroch", | |
| "suffix": "" | |
| } | |
| ], | |
| "year": 1989, | |
| "venue": "", | |
| "volume": "", | |
| "issue": "", | |
| "pages": "66--98", | |
| "other_ids": {}, | |
| "num": null, | |
| "urls": [], | |
| "raw_text": "A.S. Kroch. 1989. Asymmetries in Long-Distance Extraction. In M.R. Baltin & A.S. Kroch, eds., Alternative Conceptions of Phrase Structure., 66-98. Chicago and London: University of Chicago Press.", | |
| "links": null | |
| }, | |
| "BIBREF6": { | |
| "ref_id": "b6", | |
| "title": "On the calculus of syntactic types", | |
| "authors": [ | |
| { | |
| "first": "J", | |
| "middle": [], | |
| "last": "Lambek", | |
| "suffix": "" | |
| } | |
| ], | |
| "year": 1961, | |
| "venue": "Structure of Language in its Mathematical Aspects. Proceedings of the 12th Symposium in Applied Mathematics", | |
| "volume": "", | |
| "issue": "", | |
| "pages": "", | |
| "other_ids": {}, | |
| "num": null, | |
| "urls": [], | |
| "raw_text": "J. Lambek. 1961. On the calculus of syntactic types. In R. 0. Jakobson, ed., Structure of Lan- guage in its Mathematical Aspects. Proceedings of the 12th Symposium in Applied Mathematics. American Mathematical Society, Providence.", | |
| "links": null | |
| }, | |
| "BIBREF7": { | |
| "ref_id": "b7", | |
| "title": "The non-universa.lity of a surfa.ce filter", | |
| "authors": [ | |
| { | |
| "first": "J", | |
| "middle": [], | |
| "last": "Maling", | |
| "suffix": "" | |
| }, | |
| { | |
| "first": "& A", | |
| "middle": [], | |
| "last": "Zaenen", | |
| "suffix": "" | |
| } | |
| ], | |
| "year": null, | |
| "venue": "Syntax and Semantics xx: Icelandic Syntax", | |
| "volume": "", | |
| "issue": "", | |
| "pages": "", | |
| "other_ids": {}, | |
| "num": null, | |
| "urls": [], | |
| "raw_text": "J. Maling & A. Zaenen. 19xx. The non-universa.lity of a surfa.ce filter. In J. Maling & A. Zaenen, eds., Syntax and Semantics xx: Icelandic Syntax. xxx-xxx. Orlando: Academic Press.", | |
| "links": null | |
| }, | |
| "BIBREF8": { | |
| "ref_id": "b8", | |
| "title": "Handbook of Logic and Language", | |
| "authors": [ | |
| { | |
| "first": "M", | |
| "middle": [], | |
| "last": "", | |
| "suffix": "" | |
| } | |
| ], | |
| "year": 1996, | |
| "venue": "", | |
| "volume": "", | |
| "issue": "", | |
| "pages": "", | |
| "other_ids": {}, | |
| "num": null, | |
| "urls": [], | |
| "raw_text": "M. :tvloortgat. 1996. Categorial type logics. In J. van Benthem and A. ter Meulen, eds., Hand- book of Logic and Language. Elsevier, Amsterdam.", | |
| "links": null | |
| }, | |
| "BIBREF9": { | |
| "ref_id": "b9", | |
| "title": "Categorial Grammar: Logical Parameters and Linguistic Variation. Lecture notes. European Summer School in Logic, Language, and Information", | |
| "authors": [ | |
| { | |
| "first": "", | |
| "middle": [], | |
| "last": "Ivi", | |
| "suffix": "" | |
| }, | |
| { | |
| "first": "R", | |
| "middle": [ | |
| "T" | |
| ], | |
| "last": "Moortgat", | |
| "suffix": "" | |
| }, | |
| { | |
| "first": "", | |
| "middle": [], | |
| "last": "Oehrle", | |
| "suffix": "" | |
| } | |
| ], | |
| "year": 1993, | |
| "venue": "", | |
| "volume": "", | |
| "issue": "", | |
| "pages": "", | |
| "other_ids": {}, | |
| "num": null, | |
| "urls": [], | |
| "raw_text": "IvI. Moortgat and R. T. Oehrle. 1993. Categorial Grammar: Logical Parameters and Linguistic Variation. Lecture notes. European Summer School in Logic, Language, and Information. Faculdade de Letras, Universidade de Lisboa, Portugal.", | |
| "links": null | |
| }, | |
| "BIBREF10": { | |
| "ref_id": "b10", | |
| "title": "Adjacency, dependency, order", | |
| "authors": [ | |
| { | |
| "first": "R", | |
| "middle": [ | |
| "T" | |
| ], | |
| "last": "Moortgat", | |
| "suffix": "" | |
| }, | |
| { | |
| "first": "", | |
| "middle": [], | |
| "last": "Oehrle", | |
| "suffix": "" | |
| } | |
| ], | |
| "year": 1993, | |
| "venue": "Proceedings of the Ninth Amsterdam Colloquium. 447-467. Institute for Logic, Language, and Computation", | |
| "volume": "", | |
| "issue": "", | |
| "pages": "", | |
| "other_ids": {}, | |
| "num": null, | |
| "urls": [], | |
| "raw_text": "l'vl. Moortgat and R. T. Oehrle. 1993. Adjacency, dependency, order. P. Dekker & M. Stokhof, eds. Proceedings of the Ninth Amsterdam Colloquium. 447-467. Institute for Logic, Language, and Computation, Universiteit van Amsterdam.", | |
| "links": null | |
| }, | |
| "BIBREF11": { | |
| "ref_id": "b11", | |
| "title": "Type Logical Grammar: Categorial Logic of Signs", | |
| "authors": [ | |
| { | |
| "first": "G", | |
| "middle": [], | |
| "last": "", | |
| "suffix": "" | |
| } | |
| ], | |
| "year": 1994, | |
| "venue": "", | |
| "volume": "", | |
| "issue": "", | |
| "pages": "", | |
| "other_ids": {}, | |
| "num": null, | |
| "urls": [], | |
| "raw_text": "G. 1vlorrill. 1994. Type Logical Grammar: Categorial Logic of Signs. Kluwer, Dordrecht.", | |
| "links": null | |
| }, | |
| "BIBREF12": { | |
| "ref_id": "b12", | |
| "title": "Discontinuity in Categorial Grammar. Linguistics f3 Philosophy 18", | |
| "authors": [ | |
| { | |
| "first": "G", | |
| "middle": [], | |
| "last": "Morrill", | |
| "suffix": "" | |
| } | |
| ], | |
| "year": 1995, | |
| "venue": "", | |
| "volume": "", | |
| "issue": "", | |
| "pages": "175--219", | |
| "other_ids": {}, | |
| "num": null, | |
| "urls": [], | |
| "raw_text": "G. Morrill. 1995. Discontinuity in Categorial Grammar. Linguistics f3 Philosophy 18.175-219.", | |
| "links": null | |
| }, | |
| "BIBREF13": { | |
| "ref_id": "b13", | |
| "title": "Substructural logic and linguistic inference", | |
| "authors": [ | |
| { | |
| "first": "R", | |
| "middle": [ | |
| "T" | |
| ], | |
| "last": "Oehrle", | |
| "suffix": "" | |
| } | |
| ], | |
| "year": 1997, | |
| "venue": "", | |
| "volume": "", | |
| "issue": "", | |
| "pages": "", | |
| "other_ids": {}, | |
| "num": null, | |
| "urls": [], | |
| "raw_text": "R.T. Oehrle. 1997. Substructural logic and linguistic inference. Under review.", | |
| "links": null | |
| }, | |
| "BIBREF14": { | |
| "ref_id": "b14", | |
| "title": "Deep and Surface Constraints in Syntex", | |
| "authors": [ | |
| { | |
| "first": "Djvl", | |
| "middle": [], | |
| "last": "Perlmutter", | |
| "suffix": "" | |
| } | |
| ], | |
| "year": 1968, | |
| "venue": "", | |
| "volume": "", | |
| "issue": "", | |
| "pages": "", | |
| "other_ids": {}, | |
| "num": null, | |
| "urls": [], | |
| "raw_text": "DJvL Perlmutter. 1968. Deep and Surface Constraints in Syntex. Ph.D. dissertation. MIT.", | |
| "links": null | |
| }, | |
| "BIBREF15": { | |
| "ref_id": "b15", | |
| "title": "Deep and Surface Constraints in Syntax", | |
| "authors": [ | |
| { | |
| "first": "D", | |
| "middle": [ | |
| "Rvi" | |
| ], | |
| "last": "Perlmutter", | |
| "suffix": "" | |
| } | |
| ], | |
| "year": 1971, | |
| "venue": "", | |
| "volume": "", | |
| "issue": "", | |
| "pages": "", | |
| "other_ids": {}, | |
| "num": null, | |
| "urls": [], | |
| "raw_text": "D.rvI. Perlmutter. 1971. Deep and Surface Constraints in Syntax. New York: Holt, Rinehart & Vlinston.", | |
| "links": null | |
| }, | |
| "BIBREF16": { | |
| "ref_id": "b16", | |
| "title": "Denotational Semantics: The Scott-Strachey Approach to Programming Language Theory", | |
| "authors": [ | |
| { | |
| "first": "J", | |
| "middle": [], | |
| "last": "Stoy", | |
| "suffix": "" | |
| } | |
| ], | |
| "year": 1981, | |
| "venue": "", | |
| "volume": "", | |
| "issue": "", | |
| "pages": "", | |
| "other_ids": {}, | |
| "num": null, | |
| "urls": [], | |
| "raw_text": "J. Stoy. 1981. Denotational Semantics: The Scott-Strachey Approach to Programming Lan- guage Theory. Cambridge, Mass. & London: MIT Press.", | |
| "links": null | |
| } | |
| }, | |
| "ref_entries": { | |
| "FIGREF0": { | |
| "type_str": "figure", | |
| "num": null, | |
| "text": "f-Marie\u2022 (a \u2022 (dit \u2022 (que \u2022 (Jean \u2022 (a \u2022 (vu \u2022(Martin)))))))::::} s f-Jean \u2022 (said \u2022 (that \u2022 (Martin\u2022 (saw \u2022 Marie))))::::} s f-zei \u2022(Marie\u2022 (dat \u2022 (Martin \u2022 ((die appel \u2022 gegeten) \u2022 heeft))))::::} is", | |
| "uris": null | |
| }, | |
| "FIGREF1": { | |
| "type_str": "figure", | |
| "num": null, | |
| "text": "2 .. to show that the body is of type e\\s, we rnust be able to show e \u2022 [body) => s \u2022 This step requires communication between the hypothetical premise e and the position of the gap inside the body of the embedded question; 3. communication between the hypothetical premise e and the position of the gap must be statable by logical principles; and 4. the additional logical principles allowing communication between the hypothetical premise ~ and the position of the gap must not lead to overgeneration (as occurs if we extend our logical system from NL to LP by adding both the Associativity Rules and Permutation; while this would a!low communication between the hypothetical premise ~ and any possible position in the body, it would also completely destroy the possibility of distinguishing expressions by the order of their components (just as the associativity rules destroy the possibility of distinguish expressions by the grouping of sub-expressions)).", | |
| "uris": null | |
| }, | |
| "FIGREF2": { | |
| "type_str": "figure", | |
| "num": null, | |
| "text": "(cq/(<>whD~h np\\s) \u2022 np\\s) ==* cq. lt is worth seeing how the proof of this theorem unfolds, in order to appreciate the deductive role played by the modalities. ! unary a!, r a, r <>whDwhnp ==* np np\u2022 (np\\s) \"* s ------------------t (<>whD~hnp \u2022 (np\\s)) \"* s ----------a a, r np\\s => <>w1tD~hnp\\s (cq/((<>whD~hnp)\\s) \u2022 (<>whD~hnp)\\s) => cq ---------'---'--------------__;,;;.;\"'-------__;,;;.;..;.._ ___ ~ t (cq/((<>w1tD~hnp)\\s) \u2022 np\\s) => cq", | |
| "uris": null | |
| }, | |
| "FIGREF3": { | |
| "type_str": "figure", | |
| "num": null, | |
| "text": "2r <>whA \u2022 (B \u2022 C) => B \u2022 (C \u2022 <>whA) K lr ((A \u2022 B) \u2022 <>C) => ((A \u2022 <>C) \u2022 B) ,___ K 2r ((A \u2022 B) \u2022 <>C) => (A \u2022 (B \u2022 <>C)) postulates for French and English --+ K 2l <>whA \u2022 (B \u2022 C) => B \u2022 (<>whA \u2022 C) K 1l <>A. (B. C) => (<>A.B). c postulates for Dutch", | |
| "uris": null | |
| }, | |
| "FIGREF4": { | |
| "type_str": "figure", | |
| "num": null, | |
| "text": "Marie (said ((that oolnp)(saw Martin)))) If_ lr (Marie ((said (that (saw Martin))) oolnp)) ~ 2 r oolnp(Marie (said (that (saw Martin)))) K 2 r", | |
| "uris": null | |
| }, | |
| "TABREF1": { | |
| "html": null, | |
| "text": "Applying the unary adjointness law in this case, we have But this is just another way of writ.ing A \u2022 B =? C iff B * A\\C Similarly, we can write A \u2022 B as the unary operator <>B applied to A, and regard C/ B as o1c. Applying the unary adjointness law here gives A \u2022 B =? c iff A =? c I B. que-clause 1 dat-c1ause The full set of formulae (categories) is obtained as usual by closing the set of atoms under the binary type constructors \u2022, /, and \\. The lexical declarations we need are given in the table below: 5 is extended to binarily bmcketed sequences of words in the Standard way: thus, if I is an appropriate index set and niEJ Wi is a binarily bracketed sequence of words and T is a formula, if there are categories {Ti }iEJ such thatw l-Wi => TiThe first four Iines come directly from our lexical assumptions; the final line can be straightforwardly demonstrated as displayed in the proof tree below, where inference steps are marked with t, a, or r, according to whcthcr they depend on transitivity, adjointness, or reftexivity, respectively. 6", | |
| "type_str": "table", | |
| "num": null, | |
| "content": "<table><tr><td colspan=\"2\">atom vernacular category s sentence For example, we havc</td><td/></tr><tr><td>is f s</td><td colspan=\"3\">inverted sentence verb-final clause NL, fr*nch f-Jean \u2022 (a \u2022 (vu \u2022(Martin)))=} s</td></tr><tr><td>np because</td><td colspan=\"2\">noun phrase (including proper names)</td></tr><tr><td colspan=\"4\">partp participle phrase c fr*nch f-Jean =} np fr*nch f-a::::} (np\\s)/partp fr*nch f-vu ::::} partp/np fr*nch f-Martin ::::} np AND that-clause, language category lexical inhabitants fr*nch np Marie, Jean, Martin NL f-(np \u2022 ((np\\s)/partp \u2022 (partp/np \u2022 np))) ::::} s</td></tr><tr><td/><td>( np\\s) /pa.rtp</td><td>a</td></tr><tr><td/><td>partp/np</td><td>vu</td></tr><tr><td/><td>partp/c</td><td>dit</td></tr><tr><td colspan=\"2\">c/s ~~~~~~~~~ a,r</td><td>que</td><td>a,r</td></tr><tr><td colspan=\"4\">*ngl*sh np partp/np \u2022 np::::} partp ~~~~~~~~~~~~~~~~~~~~~~~-t (np\\s)/partp \u2022 pm\u2022tp::::} np\\s Marie, Jean, Martin (np\\s)/np (np\\s )/pa.rtp \u2022 (pm\u2022tp/np \u2022 np) ::::} np\\s saw c/ s that (np \u2022 ((np\\s)/partp \u2022 (partp/np \u2022 np)))::::} s np \u2022 np\\s ::::} s</td><td>a,r t</td></tr><tr><td colspan=\"3\">(np\\s)/c Similarly, as the reader is invited to show, we have: said</td></tr><tr><td/><td colspan=\"2\">((np\\s)/(np\\s))/np said</td></tr><tr><td colspan=\"2\">NL,fr*nch</td><td/></tr><tr><td colspan=\"2\">d*tch NL, *ngl*sh np</td><td>Marie, Martin, die appel</td></tr><tr><td colspan=\"2\">np\\partp NL,d*tch</td><td>opgegeten, gezien</td></tr><tr><td/><td>np\\ (partp\\f s)</td><td>heeft</td></tr><tr><td/><td>c/fs</td><td>dat</td></tr><tr><td/><td>(is/c)/np</td><td/></tr><tr><td>and</td><td/><td/></tr><tr><td colspan=\"4\">To show both dependencies, we may indicate that such a situation holds by</td></tr></table>" | |
| } | |
| } | |
| } | |
| } |