{ "paper_id": "P08-1038", "header": { "generated_with": "S2ORC 1.0.0", "date_generated": "2023-01-19T08:34:22.861280Z" }, "title": "A Logical Basis for the D Combinator and Normal Form in CCG", "authors": [ { "first": "Frederick", "middle": [], "last": "Hoyt", "suffix": "", "affiliation": { "laboratory": "", "institution": "The University of Texas at Austin", "location": {} }, "email": "fmhoyt@mail.utexas.edu" }, { "first": "Jason", "middle": [], "last": "Baldridge", "suffix": "", "affiliation": { "laboratory": "", "institution": "The University of Texas at Austin", "location": {} }, "email": "jbaldrid@mail.utexas.edu" } ], "year": "", "venue": null, "identifiers": {}, "abstract": "The standard set of rules defined in Combinatory Categorial Grammar (CCG) fails to provide satisfactory analyses for a number of syntactic structures found in natural languages. These structures can be analyzed elegantly by augmenting CCG with a class of rules based on the combinator D (Curry and Feys, 1958). We show two ways to derive the D rules: one based on unary composition and the other based on a logical characterization of CCG's rule base (Baldridge, 2002). We also show how Eisner's (1996) normal form constraints follow from this logic, ensuring that the D rules do not lead to spurious ambiguities.", "pdf_parse": { "paper_id": "P08-1038", "_pdf_hash": "", "abstract": [ { "text": "The standard set of rules defined in Combinatory Categorial Grammar (CCG) fails to provide satisfactory analyses for a number of syntactic structures found in natural languages. These structures can be analyzed elegantly by augmenting CCG with a class of rules based on the combinator D (Curry and Feys, 1958). We show two ways to derive the D rules: one based on unary composition and the other based on a logical characterization of CCG's rule base (Baldridge, 2002). We also show how Eisner's (1996) normal form constraints follow from this logic, ensuring that the D rules do not lead to spurious ambiguities.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Abstract", "sec_num": null } ], "body_text": [ { "text": "Combinatory Categorial Grammar (CCG, Steedman (2000) ) is a compositional, semantically transparent formalism that is both linguistically expressive and computationally tractable. It has been used for a variety of tasks, such as wide-coverage parsing (Hockenmaier and Steedman, 2002; Clark and Curran, 2007) , sentence realization (White, 2006) , learning semantic parsers (Zettlemoyer and Collins, 2007) , dialog systems (Kruijff et al., 2007) , grammar engineering (Beavers, 2004; Baldridge et al., 2007) , and modeling syntactic priming (Reitter et al., 2006) .", "cite_spans": [ { "start": 31, "end": 52, "text": "(CCG, Steedman (2000)", "ref_id": null }, { "start": 268, "end": 283, "text": "Steedman, 2002;", "ref_id": "BIBREF14" }, { "start": 284, "end": 307, "text": "Clark and Curran, 2007)", "ref_id": "BIBREF8" }, { "start": 331, "end": 344, "text": "(White, 2006)", "ref_id": "BIBREF29" }, { "start": 373, "end": 404, "text": "(Zettlemoyer and Collins, 2007)", "ref_id": "BIBREF31" }, { "start": 422, "end": 444, "text": "(Kruijff et al., 2007)", "ref_id": "BIBREF18" }, { "start": 467, "end": 482, "text": "(Beavers, 2004;", "ref_id": "BIBREF5" }, { "start": 483, "end": 506, "text": "Baldridge et al., 2007)", "ref_id": "BIBREF3" }, { "start": 540, "end": 562, "text": "(Reitter et al., 2006)", "ref_id": "BIBREF24" } ], "ref_spans": [], "eq_spans": [], "section": "Introduction", "sec_num": "1" }, { "text": "A distinctive aspect of CCG is that it provides a very flexible notion of constituency. This supports elegant analyses of several phenomena (e.g., coordination, long-distance extraction, and intonation) and allows incremental parsing with the competence grammar (Steedman, 2000) . Here, we argue that even with its flexibility, CCG as standardly defined is not permissive enough for certain linguistic constructions and greater incrementality. Following Wittenburg (1987) , we remedy this by adding a set of rules based on the D combinator of combinatory logic (Curry and Feys, 1958) .", "cite_spans": [ { "start": 262, "end": 278, "text": "(Steedman, 2000)", "ref_id": "BIBREF27" }, { "start": 454, "end": 471, "text": "Wittenburg (1987)", "ref_id": "BIBREF30" }, { "start": 561, "end": 583, "text": "(Curry and Feys, 1958)", "ref_id": "BIBREF9" } ], "ref_spans": [], "eq_spans": [], "section": "Introduction", "sec_num": "1" }, { "text": "(1) x/(y/z) :f y/w : g \u21d2 x/(w/z): \u03bbh.f (\u03bbx.ghx)", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Introduction", "sec_num": "1" }, { "text": "We show that CCG augmented with this rule improves CCG's empirical coverage by allowing better analyses of modal verbs in English and causatives in Spanish, and certain coordinate constructions.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Introduction", "sec_num": "1" }, { "text": "The D rules are well-behaved; we show this by deriving them both from unary composition and from the logic defined by Baldridge (2002) . Both perspectives on D ensure that the new rules are compatible with normal form constraints (Eisner, 1996) for controlling spurious ambiguity. The logic also ensures that the new rules are subject to modalities consistent with those defined by Baldridge and Kruijff (2003) . Furthermore, we define a logic that produces Eisner's constraints as grammar internal theorems rather than parsing stipulations.", "cite_spans": [ { "start": 118, "end": 134, "text": "Baldridge (2002)", "ref_id": "BIBREF4" }, { "start": 230, "end": 244, "text": "(Eisner, 1996)", "ref_id": "BIBREF10" }, { "start": 382, "end": 410, "text": "Baldridge and Kruijff (2003)", "ref_id": "BIBREF2" } ], "ref_spans": [], "eq_spans": [], "section": "Introduction", "sec_num": "1" }, { "text": "CCG uses a universal set of syntactic rules based on the B, T, and S combinators of combinatory logic (Curry and Feys, 1958) :", "cite_spans": [ { "start": 102, "end": 124, "text": "(Curry and Feys, 1958)", "ref_id": "BIBREF9" } ], "ref_spans": [], "eq_spans": [], "section": "Combinatory Categorial Grammar", "sec_num": "2" }, { "text": "(2) B: ((Bf )g)x = f (gx)", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Combinatory Categorial Grammar", "sec_num": "2" }, { "text": "T: Txf = f x S: ((Sf )g)x = f x(gx)", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Combinatory Categorial Grammar", "sec_num": "2" }, { "text": "CCG functors are functions over strings of symbols, so different linearized versions of each of the combinators have to be specified (ignoring S here):", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Combinatory Categorial Grammar", "sec_num": "2" }, { "text": "(3) FA:", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Combinatory Categorial Grammar", "sec_num": "2" }, { "text": "(>) x/ y y \u21d2 x (<) y x\\ y \u21d2 x B: (>B) x/ y y/ z \u21d2 x/ z (B \u00d7 ) x/ \u00d7 y y\\ \u00d7 z \u21d2 x\\ \u00d7 z (T) x \u21d2 t/ i (t\\ i x) (B-rule, deriving two composed constituents that are arguments to the conjunction: 1 (6) i. Bob s/(s\\np) 1 We follow (Steedman, 2000) in assuming that type-raising applies in the lexicon, and therefore that nominals such as Stan ii. Stan, Max ((s\\np)/np)\\(((s\\np)/np)/np) iii. a beer, a coke (s\\np)\\((s\\np)/np) iv. and Similarly, I will buy is derived with category s/np by assuming the category (6i) for I and composing that with both verbs in turn.", "cite_spans": [ { "start": 505, "end": 506, "text": "1", "ref_id": null }, { "start": 517, "end": 533, "text": "(Steedman, 2000)", "ref_id": "BIBREF27" } ], "ref_spans": [], "eq_spans": [], "section": "Combinatory Categorial Grammar", "sec_num": "2" }, { "text": "(x\\ x)/ x v", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Combinatory Categorial Grammar", "sec_num": "2" }, { "text": "CCG's approach is appealing because such constituents are not odd at all: they simply follow from the fact that CCG is a system of type-based grammatical inference that allows left associativity.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Combinatory Categorial Grammar", "sec_num": "2" }, { "text": "CCG is only partially associative. Here, we discuss several situations which require greater associativity and thus cannot be given an adequate analysis with CCG as standardly defined. These structures have in common that a category of the form x|(y|z) must combine with one of the form y|w-exactly the configuration handled by the D schemata in (1).", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Linguistic Motivation for D", "sec_num": "3" }, { "text": "In the first situation, a question word is distributed across auxiliary or subordinating verb categories: We call this cross-conjunct extraction. It was noted by Pickering and Barry (1993) for English, but to the best of our knowledge it has not been treated in the have type-raised lexical assignments. We also suppress semantic representations in the derivations for the sake of space.", "cite_spans": [ { "start": 162, "end": 188, "text": "Pickering and Barry (1993)", "ref_id": "BIBREF23" } ], "ref_spans": [], "eq_spans": [], "section": "Cross-Conjunct Extraction", "sec_num": "3.1" }, { "text": "CCG literature, nor noted in other languages. The problem it presents to CCG is clear in (11), which shows the necessary derivation of (10) using standard multimodal category assignments. For the tokens of what to form constituents with you can and you must not, they must must combine directly. The problem is that these constituents (in bold) cannot be created with the standard CCG combinators in (3). The category for and is marked for non-associativity with , and thus combines with other expressions only by function application (Baldridge, 2002) . This ensures that each conjunct is a discrete constituent.", "cite_spans": [ { "start": 535, "end": 552, "text": "(Baldridge, 2002)", "ref_id": "BIBREF4" } ], "ref_spans": [], "eq_spans": [], "section": "Cross-Conjunct Extraction", "sec_num": "3.1" }, { "text": "Cross-conjunct extraction occurs in other languages as well, including Dutch (12), German (13), Romanian (14), and Spanish 15 It is thus a general phenomenon, not just a quirk of English. While it could be handled with extra categories, such as (s/(vp/np))/(s/np) for what, this is exactly the sort of strong-arm tactic that inclusion of the standard B, T, and S rules is meant to avoid.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Cross-Conjunct Extraction", "sec_num": "3.1" }, { "text": "The standard CCG analysis for English auxiliary verbs is the type exemplified in (16) (Steedman, 2000, 68) , interpreted as a unary operator over sentence meanings (Gamut, 1991; Kratzer, 1991) :", "cite_spans": [ { "start": 86, "end": 106, "text": "(Steedman, 2000, 68)", "ref_id": null }, { "start": 164, "end": 177, "text": "(Gamut, 1991;", "ref_id": "BIBREF12" }, { "start": 178, "end": 192, "text": "Kratzer, 1991)", "ref_id": "BIBREF18" } ], "ref_spans": [], "eq_spans": [], "section": "English Auxiliary Verbs", "sec_num": "3.2" }, { "text": "(16) can (s\\np)/(s\\np) : \u03bbP et \u03bbx.\u2666P (x)", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "English Auxiliary Verbs", "sec_num": "3.2" }, { "text": "However, this type is empirically underdetermined, given a widely-noted set of generalizations suggesting that auxiliaries and raising verbs take no subject argument at all (Jacobson, 1990, a.o.) . 17i. Lack of syntactic restrictions on the subject;", "cite_spans": [ { "start": 173, "end": 195, "text": "(Jacobson, 1990, a.o.)", "ref_id": null } ], "ref_spans": [], "eq_spans": [], "section": "English Auxiliary Verbs", "sec_num": "3.2" }, { "text": "ii. Lack of semantic restrictions on the subject;", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "English Auxiliary Verbs", "sec_num": "3.2" }, { "text": "iii. Inheritance of selectional restrictions from the subordinate predicate.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "English Auxiliary Verbs", "sec_num": "3.2" }, { "text": "Two arguments are made for (16). First, it is necessary so that type-raised subjects can compose with the auxiliary in extraction contexts, as in 18:", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "English Auxiliary Verbs", "sec_num": "3.2" }, { "text": "(18) what I can eat s/(s/np) s/vp vp/vp tv >B s/vp >B s/np > s", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "English Auxiliary Verbs", "sec_num": "3.2" }, { "text": "Second, it is claimed to be necessary in order to account for subject-verb agreement, on the assumption that agreement features are domain restrictions on functors of type s\\np (Steedman, 1992 (Steedman, , 1996 . The first argument is the topic of this paper, and, as we show below, is refuted by the use of the Dcombinator. The second argument is undermined by examples like (19): In (19), appear agrees with two negative-polaritysensitive NPs trapped inside a neither-nor coordinate structure in which they are licensed. Appear therefore does not combine with them directly, showing that the agreement relation need not be mediated by direct application of a subject argument. We conclude, therefore, that the assignment of the vp/vp type to English auxiliaries and modal verbs is unsupported on both formal and linguistic grounds.", "cite_spans": [ { "start": 177, "end": 192, "text": "(Steedman, 1992", "ref_id": null }, { "start": 193, "end": 210, "text": "(Steedman, , 1996", "ref_id": "BIBREF26" } ], "ref_spans": [], "eq_spans": [], "section": "English Auxiliary Verbs", "sec_num": "3.2" }, { "text": "Following Jacobson (1990) , a more empiricallymotivated assignment is (20):", "cite_spans": [ { "start": 10, "end": 25, "text": "Jacobson (1990)", "ref_id": "BIBREF15" } ], "ref_spans": [], "eq_spans": [], "section": "English Auxiliary Verbs", "sec_num": "3.2" }, { "text": "(20) can s/s : \u03bbp t .\u2666p", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "English Auxiliary Verbs", "sec_num": "3.2" }, { "text": "Combining (20) with a type-raised subject presents another instance of the structure in (1), where that question words are represented as variable-binding operators (Groenendijk and Stokhof, 1997 The aspect of the construction that is relevant here is that the causative verb hacer appears to take an object argument understood as the subject or agent of the subordinate verb (the causee). However, it has been argued that Spanish causative verbs do not in fact take objects (Ackerman and Moore, 1999 , and refs therein). There are two arguments for this.", "cite_spans": [ { "start": 165, "end": 195, "text": "(Groenendijk and Stokhof, 1997", "ref_id": "BIBREF13" }, { "start": 475, "end": 500, "text": "(Ackerman and Moore, 1999", "ref_id": "BIBREF0" } ], "ref_spans": [], "eq_spans": [], "section": "English Auxiliary Verbs", "sec_num": "3.2" }, { "text": "First, syntactic alternations that apply to objecttaking verbs, such as passivization and periphrasis with subjunctive complements, do not apply to hacer (Luj\u00e1n, 1980) . Second, hacer specifies neither the case form of the causee, nor any semantic entailments with respect to it. These are instead determined by syntactic, semantic, and pragmatic factors, such as transitivity, word order, animacy, gender, social prestige, and referential specificity (Finnemann, 1982, a.o) . Thus, there is neither syntactic nor semantic evidence that hacer takes an object argument.", "cite_spans": [ { "start": 154, "end": 167, "text": "(Luj\u00e1n, 1980)", "ref_id": "BIBREF20" }, { "start": 452, "end": 474, "text": "(Finnemann, 1982, a.o)", "ref_id": null } ], "ref_spans": [], "eq_spans": [], "section": "English Auxiliary Verbs", "sec_num": "3.2" }, { "text": "On this basis, we assign hacer the category (23):", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "English Auxiliary Verbs", "sec_num": "3.2" }, { "text": "(23) hacer (s\\np)/s : \u03bbP \u03bbx.cause P x", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "English Auxiliary Verbs", "sec_num": "3.2" }, { "text": "However, Spanish has examples of cross-conjunct extraction in which hacer hosts clitics: This shows another instance of the schema in (1), which is undefined for any of the combinators in 3 ", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "English Auxiliary Verbs", "sec_num": "3.2" }, { "text": "The preceding data motivates adding D rules (we return to the distribution of the modalities below):", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Analyses Based on D", "sec_num": "3.4" }, { "text": "(26) >D x/ (y/ z) y/ w \u21d2 x/ (w/ z) >D \u00d7 x/ \u00d7 (y/ \u00d7 z) y\\ \u00d7 w \u21d2 x\\ \u00d7 (w/ \u00d7 z) >D \u00d7 x/ (y\\ \u00d7 z) y/ \u2022 w \u21d2 x/ (w\\ \u00d7 z) >D \u00d7 x/ \u00d7 (y\\ z) y\\ \u2022 w \u21d2 x\\ \u00d7 (w\\ z) (27) D allows you and can to combine when the auxiliary is given the principled type assignment s/s, and another combines what with the result.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Analyses Based on D", "sec_num": "3.4" }, { "text": "(28) what you can s/ (s/ np) s/ (s\\ \u00d7 np) s/ \u2022 s >D \u00d7 s/ (s\\ \u00d7 np) >D s/ ((s\\ \u00d7 np)/ np)", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Analyses Based on D", "sec_num": "3.4" }, { "text": "The derivation then proceeds in the usual way. Likewise, D handles the Spanish causative constructions (29) straightforwardly :", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Analyses Based on D", "sec_num": "3.4" }, { "text": "(29) lo hice dormir (s\\np)/ ((s\\np)/ np) (s\\np)/ s s/np >D (s\\np)/ (s/ np) > s\\np", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Analyses Based on D", "sec_num": "3.4" }, { "text": "The D-rules thus provide straightforward analyses of such constructions by delivering flexible constituency while maintaining CCG's committment to low categorial ambiguity and semantic transparency.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Analyses Based on D", "sec_num": "3.4" }, { "text": "Adding new rules can have implications for parsing efficiency. In this section, we show that the D rules fit naturally within standard normal form constraints for CCG parsing (Eisner, 1996) , by providing both combinatory and logical bases for D. This additionally allows Eisner's normal form constraints to be derived as grammar internal theorems.", "cite_spans": [ { "start": 175, "end": 189, "text": "(Eisner, 1996)", "ref_id": "BIBREF10" } ], "ref_spans": [], "eq_spans": [], "section": "Deriving Eisner Normal Form", "sec_num": "4" }, { "text": "CCG's flexibility is useful for linguistic analyses, but leads to spurious ambiguity (Wittenburg, 1987) due to the associativity introduced by the B and T rules. This can incur a high computational cost which parsers must deal with. Several techniques have been proposed for the problem (Wittenburg, 1987; Karttunen, 1989; Hepple and Morrill, 1989; Eisner, 1996) . The most commonly used are Karttunnen's chart subsumption check (White and Baldridge, 2003; Hockenmaier and Steedman, 2002 ) and Eisner's normal-form constraints (Bozsahin, 1998; Clark and Curran, 2007 ).", "cite_spans": [ { "start": 85, "end": 103, "text": "(Wittenburg, 1987)", "ref_id": "BIBREF30" }, { "start": 287, "end": 305, "text": "(Wittenburg, 1987;", "ref_id": "BIBREF30" }, { "start": 306, "end": 322, "text": "Karttunen, 1989;", "ref_id": "BIBREF17" }, { "start": 323, "end": 348, "text": "Hepple and Morrill, 1989;", "ref_id": null }, { "start": 349, "end": 362, "text": "Eisner, 1996)", "ref_id": "BIBREF10" }, { "start": 429, "end": 456, "text": "(White and Baldridge, 2003;", "ref_id": "BIBREF28" }, { "start": 457, "end": 487, "text": "Hockenmaier and Steedman, 2002", "ref_id": "BIBREF14" }, { "start": 527, "end": 543, "text": "(Bozsahin, 1998;", "ref_id": "BIBREF7" }, { "start": 544, "end": 566, "text": "Clark and Curran, 2007", "ref_id": "BIBREF8" } ], "ref_spans": [], "eq_spans": [], "section": "The Spurious Ambiguity Problem", "sec_num": "4.1" }, { "text": "Eisner's normal form, referred to here as Eisner NF and paraphrased in (30), has the advantage of not requiring comparisons of logical forms: it functions purely on the syntactic types being combined.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "The Spurious Ambiguity Problem", "sec_num": "4.1" }, { "text": "(30) For a set S of semantically equivalent 2 parse trees for a string ABC, admit the unique parse tree such that at least one of (i) or (ii) holds:", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "The Spurious Ambiguity Problem", "sec_num": "4.1" }, { "text": "i. C is not the argument of (AB) resulting from application of >B 1 + . ii. A is not the argument of (BC) resulting from application of B n :", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "The Spurious Ambiguity Problem", "sec_num": "4.1" }, { "text": "x/y y$ n \u21d2 x$ n (34) B (x/z)/(y/z) > x/z B n (n \u2265 1)", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Deriving D from B", "sec_num": "4.2" }, { "text": "is derived by applyingB to the primary functor n times. For example, B 2 is derived by 2 applications ofB to the primary functor:", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Deriving D from B", "sec_num": "4.2" }, { "text": "(40) \u2206 \u0393 x/y (y/w)/\u1e91 B (x/w)/(y/w)B ((x/w)/z)/((y/w)/z) > (x/w)/z", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Deriving D from B", "sec_num": "4.2" }, { "text": "The rules for D correspond to application ofB to both the primary and secondary functors, followed by function application:", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Deriving D from B", "sec_num": "4.2" }, { "text": "(41) \u2206 \u0393 x/(y/z) y/w >B >B (x/(w/z))/((y/z)/(w/z)) (y/z)/(w/z) > x/(w/z)", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Deriving D from B", "sec_num": "4.2" }, { "text": "As with B n , D n\u22651 can be derived by iterative application ofB to both primary and secondary functors. Because B can be derived fromB, clause (iii) of (35) is equivalent to the following:", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Deriving D from B", "sec_num": "4.2" }, { "text": "(42) If \u03b2 is not in Eisner-NF, then N F (\u03b2) = F A, B , \u03b2 1 , \u03b2 2 , such that N F (\u03b1) = S, \u03b2 1 , N F ( T, \u03b2 2 , \u03b3 )", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Deriving D from B", "sec_num": "4.2" }, { "text": "Interpreted in terms ofB, both B and D involve application ofB to the primary functor. It follows that Theorem I applies directly to D simply by virtue of the equivalence between binary B and unary-B+FA. Eisner's NF constraints can then be reinterpreted as a constraint onB requiring its output to be an inert result category. We represent this in terms of theBrules introducing an inert slash, indicated with \"!\" (adopting the convention from OpenCCG):", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Deriving D from B", "sec_num": "4.2" }, { "text": "(43) x/y : f xy \u21d2 (x/ ! z)/(y/ ! z) : \u03bbh zy \u03bbx z f hx", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Deriving D from B", "sec_num": "4.2" }, { "text": "Hence, both binary B and D return inert functors:", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Deriving D from B", "sec_num": "4.2" }, { "text": "(44) \u2206 \u0393 x/y y/z >B (x/ ! z)/(y/ ! z) > x/ ! z (45) \u2206 \u0393 x/(y/z) y/w >B >B (x/ ! (w/z))/((y/z)/ ! (w/z)) (y/ ! z)/(w/ ! z) > x/ ! (w/z)", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Deriving D from B", "sec_num": "4.2" }, { "text": "The binary substitution (S) combinator can be similarly incorporated into the system. Unary sub-stitution\u015c is likeB except that it introduces a slash on only the argument-side of the input functor. We stipulate that\u015c returns a category with inert slashes:", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Deriving D from B", "sec_num": "4.2" }, { "text": "(46) (\u015c) (x/y)/z \u21d2 (x/ ! z)/(y/ ! z)", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Deriving D from B", "sec_num": "4.2" }, { "text": "T is by definition unary. It follows that all the binary rules in CCG (including the D-rules) can be reduced to (iterated) instantiations of the unary combinator\u015d B,\u015c, or T plus function application. This provides a basis for CCG in which all combinatory rules are derived from unaryB\u015c, and T.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Deriving D from B", "sec_num": "4.2" }, { "text": "The previous section shows that deriving CCG rules from unary combinators allows us to derive the Drules while preserving Eisner NF. In this section, we present an alternate formulation of Eisner NF with Baldridge's (2002) CTL basis for CCG. This formulation allows us to derive the D-rules as before, and does so in a way that seamlessly integrates with Baldridge's system of modalized functors.", "cite_spans": [ { "start": 204, "end": 222, "text": "Baldridge's (2002)", "ref_id": "BIBREF4" } ], "ref_spans": [], "eq_spans": [], "section": "A Logical Basis for Eisner Normal Form", "sec_num": "4.3" }, { "text": "In CTL, B and B \u00d7 are proofs derived via structural rules that allow associativity and permutation of symbols within a sequent, in combination with the slash introduction and elimination rules of the base logic. To control application of these rules, Baldridge keys them to binary modal operators (for associativity) and \u00d7 (for permutation). Given these, >B is proven in (47):", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "A Logical Basis for Eisner Normal Form", "sec_num": "4.3" }, { "text": "(47) \u2206 x/ y \u0393 y/ z [a z] [/ E] (\u0393 \u2022 a i ) y [/ E] (\u2206 \u2022 (\u0393 \u2022 a i )) x [RA] ((\u2206 \u2022 \u0393) \u2022 a i ) x [/ I] (\u2206 \u2022 \u0393) x/ z", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "A Logical Basis for Eisner Normal Form", "sec_num": "4.3" }, { "text": "In a CCG ruleset compiled from such logics, a category must have an appropriately decorated slash in order to be the input to a rule. This means that rules apply universally, without language-specific restrictions. Instead, restrictions can only be declared via modalities marked on lexical categories.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "A Logical Basis for Eisner Normal Form", "sec_num": "4.3" }, { "text": "UnaryB and the D rules in 4.2 can be derived using the same logic. For example, >B can be derived as in (48):", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "A Logical Basis for Eisner Normal Form", "sec_num": "4.3" }, { "text": "(48) \u2206 x/ y [f y/ z] 1 [a z] 2 [/E] (f 1 \u2022 a 2 ) y [/ E] (\u2206 \u2022 (f 1 \u2022 a 2 )) x [RA] ((\u2206 \u2022 f 1 ) \u2022 a 2 ) x [/ I] (\u2206 \u2022 f 1 ) x/ z [/ I] \u2206 (x/ z)/ (y/ z)", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "A Logical Basis for Eisner Normal Form", "sec_num": "4.3" }, { "text": "The D rules are also theorems of this system. For example, the proof for >D applies (48) as a lemma to each of the primary and secondary functors:", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "A Logical Basis for Eisner Normal Form", "sec_num": "4.3" }, { "text": "(49) \u2206 x/ (y/ z) \u0393 y/ w >B >B \u2206 (x/ (w/ z))/ ((y/ z)/ (w/ z)) \u0393 (y/ z)/ (w/ z) [/E] (\u2206 \u2022 \u0393) x/ (w/ z)", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "A Logical Basis for Eisner Normal Form", "sec_num": "4.3" }, { "text": ">D \u00d7 involves an associative version ofB applied to the primary functor 50, and a permutative version to the secondary functor (51).", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "A Logical Basis for Eisner Normal Form", "sec_num": "4.3" }, { "text": "(50) \u2206 x/ (y\\ \u00d7 z) [f (y\\ \u00d7 z)/ \u2022 (w\\ \u00d7 z)] 1 [g w\\ \u00d7 z] 2 [/ \u2022E] (f 1 \u2022 \u2022 g 2 ) y\\ \u00d7 z [/ E] (\u2206 \u2022 (f 1 \u2022 . g 2 )) x [RA] ((\u2206 \u2022 f 1 ) \u2022 . g 2 ) x [/ \u2022I ] (\u2206 \u2022 f 1 ) x/ \u2022 (w\\ \u00d7 z) [/ I] \u2206 (x/ \u2022 (w\\ \u00d7 z))/ ((y\\ \u00d7 z)/ \u2022 (w\\ \u00d7 z)) (51) \u0393 y/ \u2022 w [a z] 1 [f w\\ \u00d7 z] 2 [\\ \u00d7 E] (a 1 \u2022 \u00d7 f 2 ) w [/ \u2022E] (\u0393 \u2022 \u2022 (a 1 \u2022 \u00d7 f 2 )) y [LP ] (a 1 \u2022 \u00d7 (\u0393 \u2022 \u2022 f 2 )) y [\\ \u00d7 I] (\u0393 \u2022 \u2022 f 2 ) y\\ \u00d7 z [/ \u2022I ] \u0393 (y\\ \u00d7 z)/ \u2022 (w\\ \u00d7 z)", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "A Logical Basis for Eisner Normal Form", "sec_num": "4.3" }, { "text": "Rules for D with appropriate modalities can therefore be incorporated seamlessly into CCG.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "A Logical Basis for Eisner Normal Form", "sec_num": "4.3" }, { "text": "In the preceding subsection, we encoded Eisner NF with inert slashes. In Baldridge's CTL basis for CCG, inert slashes are represented as functors seeking non-lexical arguments, represented as categories marked with an antecedent-governed feature, reflecting the intuition that non-lexical arguments have to be \"bound\" by a superordinate functor. This is based on an interpretation of antecedentgovernment as a unary modality \u2666 ant that allows structures marked by it to permute to the left or right periphery of a structure: 6 (52)", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "A Logical Basis for Eisner Normal Form", "sec_num": "4.3" }, { "text": "((\u2206 a \u2022 \u00d7 \u2666 ant \u2206 b ) \u2022 \u00d7 \u2206 c ) x ((\u2206 a \u2022 \u00d7 \u2206 c ) \u2022 \u00d7 \u2666 ant \u2206 b ) x [ARP] (\u2206 a \u2022 \u00d7 (\u2666 ant \u2206 b \u2022 \u00d7 \u2206 c )) x (\u2666 ant \u2206 b \u2022 \u00d7 (\u2206 a \u2022 \u00d7 \u2206 c )) x [ALP]", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "A Logical Basis for Eisner Normal Form", "sec_num": "4.3" }, { "text": "Unlike permutation rules without \u2666 ant , these permutation rules can only be used in a proof when preceeded by a hypothetical category marked with the 2 \u2193 ant modality. The elimination rule for 2 \u2193modalities introduces a corresponding \u2666-marked object in the resulting structure, feeding the rule:", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "A Logical Basis for Eisner Normal Form", "sec_num": "4.3" }, { "text": "(53) [a 2 \u2193 ant z] 1 [2 \u2193 E] \u2666 ant a 1 z \u0393 y\\ \u00d7 z [\\ \u00d7 E] \u2206 x/ \u00d7 y (\u2666 ant a 1 \u2022 \u00d7 \u0393) y [/ \u00d7 E] (\u2206 \u2022 \u00d7 (\u2666 ant a 1 \u2022 \u00d7 \u0393)) x [ALP ] [a \u2666 ant 2 \u2193 ant z] 2 (\u2666 ant a 1 \u2022 \u00d7 (\u2206 \u2022 \u00d7 \u0393)) x [\u2666E] (a \u2022 \u00d7 (\u2206 \u2022 \u00d7 \u0393)) x [\\ \u00d7 I] 2 (\u2206 \u2022 \u00d7 \u0393) x\\ \u00d7 \u2666 ant 2 \u2193 ant z", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "A Logical Basis for Eisner Normal Form", "sec_num": "4.3" }, { "text": "Re-introduction of the [a \u2666 ant 2 \u2193 ant z] k hypothesis results in a functor the argument of which is marked with \u2666 ant 2 \u2193", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "A Logical Basis for Eisner Normal Form", "sec_num": "4.3" }, { "text": "ant . Because lexical categories are not marked as such, the functor cannot take a lexical argument, and so is effectively an inert functor.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "A Logical Basis for Eisner Normal Form", "sec_num": "4.3" }, { "text": "In Baldridge's (2002) system, only proofs involving the ARP and ALP rules produce inert categories. In Eisner NF, all instances of B-rules result in inert categories. This can be reproduced in Baldridge's system simply by keying all structural rules to the ant-modality, the result being that all proofs involving structural rules result in inert functors.", "cite_spans": [ { "start": 3, "end": 21, "text": "Baldridge's (2002)", "ref_id": "BIBREF4" } ], "ref_spans": [], "eq_spans": [], "section": "A Logical Basis for Eisner Normal Form", "sec_num": "4.3" }, { "text": "As desired, the D-rules result in inert categories as well. For example, >D is derived as follows (2 \u2193 ant and \u2666 ant are abbreviated as 2 \u2193 and \u2666):", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "A Logical Basis for Eisner Normal Form", "sec_num": "4.3" }, { "text": "EQUATION", "cite_spans": [], "ref_spans": [], "eq_spans": [ { "start": 0, "end": 8, "text": "EQUATION", "ref_id": "EQREF", "raw_str": "(54) \u0393 y/ w [a 2 \u2193 (w/ z)] 1 [b 2 \u2193 z] 2 [2 \u2193 E] [2 \u2193 E] \u2666a w/ z \u2666b z [/ E] (\u2666a \u2022 \u2666b) w [/ E] (\u0393 \u2022 (\u2666a \u2022 \u2666b)) y [RA] [c \u26662 \u2193 z] 3 ((\u0393 \u2022 \u2666a) \u2022 \u2666b) y [\u2666E] 2 ((\u0393 \u2022 \u2666a) \u2022 c) y [/ I] 3 (\u0393 \u2022 \u2666a) y/ \u26662 \u2193 z (55) (54) . . . \u2206 x/ (y/ \u26662 \u2193 z) (\u0393 \u2022 \u2666a) y/ \u26662 \u2193 z [/ E] (\u2206 \u2022 (\u0393 \u2022 \u2666a)) x [RA] [d \u26662 \u2193 (w/ z)] 4 ((\u2206 \u2022 \u0393) \u2022 \u2666a) x [\u2666E] 1 ((\u2206 \u2022 \u0393) \u2022 d) x [/ I] 4 (\u2206 \u2022 \u0393) x/ \u26662 \u2193 (w/ z)", "eq_num": "(54)" } ], "section": "A Logical Basis for Eisner Normal Form", "sec_num": "4.3" }, { "text": "-(55) can be used as a lemma corresponding to the CCG rule in (57):", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "A Logical Basis for Eisner Normal Form", "sec_num": "4.3" }, { "text": "(56) \u2206 x/ (y/ \u26662 \u2193 z) \u0393 y/ w [D] (\u2206 \u2022 \u0393) x/ \u26662 \u2193 (w/ z) (57) x/ (y/ ! z) y/ w \u21d2 x/ ! (w/ z)", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "A Logical Basis for Eisner Normal Form", "sec_num": "4.3" }, { "text": "This means that all CCG rules compiled from the logic-which requires \u2666 ant to licence the structural rules necessary to prove the rules-return inert functors. Eisner NF thus falls out of the logic because all instances of B, D, and S produce inert categories. This in turns allows us to view Eisner NF as part of a theory of grammatical competence, in addition to being a useful technique for constraining parsing.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "A Logical Basis for Eisner Normal Form", "sec_num": "4.3" }, { "text": "Including the D-combinator rules in the CCG rule set lets us capture several linguistic generalizations that lack satisfactory analyses in standard CCG. Furthermore, CCG augmented with D is compatible with Eisner NF (Eisner, 1996) , a standard technique for controlling derivational ambiguity in CCG-parsers, and also with the modalized version of CCG (Baldridge and Kruijff, 2003) . A consequence is that both the D rules and the NF constraints can be derived from a grammar-internal perspective. This extends CCG's linguistic applicability without sacrificing efficiency. Wittenburg (1987) originally proposed using rules based on D as a way to reduce spurious ambiguity, which he achieved by eliminating B rules entirely and replacing them with variations on D. Wittenburg notes that doing so produces as many instances of D as there are rules in the standard rule set. Our proposal retains B and S, but, thanks to Eisner NF, eliminates spurious ambiguity, a result that Wittenburg was not able to realize at the time.", "cite_spans": [ { "start": 216, "end": 230, "text": "(Eisner, 1996)", "ref_id": "BIBREF10" }, { "start": 352, "end": 381, "text": "(Baldridge and Kruijff, 2003)", "ref_id": "BIBREF2" }, { "start": 574, "end": 591, "text": "Wittenburg (1987)", "ref_id": "BIBREF30" } ], "ref_spans": [], "eq_spans": [], "section": "Conclusion", "sec_num": "5" }, { "text": "Our approach can be incorporated into Eisner NF straightforwardly However, Eisner NF disprefers incremental analyses by forcing right-corner analyses of long-distance dependencies, such as in (58):", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Conclusion", "sec_num": "5" }, { "text": "(58) (What (does (Grommet (think (Tottie (said (Victor (knows (Wallace ate)))))))))?", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Conclusion", "sec_num": "5" }, { "text": "For applications that call for increased incrementality (e.g., aligning visual and spoken input incrementally (Kruijff et al., 2007) ), CCG rules that do not produce inert categories can be derived a CTL basis that does not require \u2666 ant for associativity and permutation. The D-rules derived from this kind of CTL specification would allow for left-corner analyses of such dependencies with the competence grammar. An extracted element can \"wrap around\" the words intervening between it and its extraction site. For example, D would allow the following bracketing for the same example (while producing the same logical form):", "cite_spans": [ { "start": 110, "end": 132, "text": "(Kruijff et al., 2007)", "ref_id": "BIBREF18" } ], "ref_spans": [], "eq_spans": [], "section": "Conclusion", "sec_num": "5" }, { "text": "(59) (((((((((What does) Grommet) think) Tottie) said) Victor) knows) Wallace) ate)?", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Conclusion", "sec_num": "5" }, { "text": "Finally, the unary combinator basis for CCG provides an interesting additional specification for generating CCG rules. Like the CTL basis, the unary combinator basis can produce a much wider range of possible rules, such as D rules, that may be relevant for linguistic applications. Whichever basis is used, inclusion of the D-rules increases empirical coverage, while at the same time preserving CCG's computational attractiveness.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Conclusion", "sec_num": "5" }, { "text": "Two parse trees are semantically equivalent if: (i) their leaf nodes have equivalent interpretations, and (ii) equivalent scope relations hold between their respective leaf-node meanings.3 http://openccg.sourceforge.net", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "", "sec_num": null }, { "text": "We useSteedman's (Steedman, 1996) \"$\"-convention for representing argument stacks of length n, for n \u2265 0.5 This isLambek's (1958) Division rule, also known as the \"Geach rule\"(Jacobson, 1999).", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "", "sec_num": null }, { "text": "Note that the diamond operator used here is a syntactic operator, rather than a semantic operator as used in (16) above. The unary modalities used in CTL describe accessibility relationships between subtypes and supertypes of particular categories: in effect, they define feature hierarchies. SeeMoortgat (1997) and Oehrle (To Appear) for further explanation.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "", "sec_num": null } ], "back_matter": [ { "text": "Thanks Mark Steedman for extensive comments and suggestions, and particularly for noting the relationship between the D-rules and unaryB. Thanks also to Emmon Bach, Cem Bozsahin, Jason Eisner, Geert-Jan Kruijff and the ACL reviewers.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Acknowledgments", "sec_num": null } ], "bib_entries": { "BIBREF0": { "ref_id": "b0", "title": "Syntagmatic and Paradigmatic Dimensions of Causee Encodings", "authors": [ { "first": "Farrell", "middle": [], "last": "Ackerman", "suffix": "" }, { "first": "John", "middle": [], "last": "Moore", "suffix": "" } ], "year": 1999, "venue": "Linguistics and Philosophy", "volume": "24", "issue": "", "pages": "1--44", "other_ids": {}, "num": null, "urls": [], "raw_text": "Farrell Ackerman and John Moore. 1999. Syntagmatic and Paradigmatic Dimensions of Causee Encodings. Linguistics and Philosophy, 24:1-44.", "links": null }, "BIBREF1": { "ref_id": "b1", "title": "Complex Predicates and Information Spreading in LFG", "authors": [ { "first": "Avery", "middle": [ "D" ], "last": "Andrews", "suffix": "" }, { "first": "Christopher", "middle": [ "D" ], "last": "Manning", "suffix": "" } ], "year": 1999, "venue": "", "volume": "", "issue": "", "pages": "", "other_ids": {}, "num": null, "urls": [], "raw_text": "Avery D. Andrews and Christopher D. Manning. 1999. Complex Predicates and Information Spreading in LFG. CSLI Publications, Palo Alto, California.", "links": null }, "BIBREF2": { "ref_id": "b2", "title": "Multi-Modal Combinatory Categorial Grammar", "authors": [ { "first": "Jason", "middle": [], "last": "Baldridge", "suffix": "" }, { "first": "Geert-Jan", "middle": [], "last": "Kruijff", "suffix": "" } ], "year": 2003, "venue": "Proceedings of EACL 10", "volume": "", "issue": "", "pages": "211--218", "other_ids": {}, "num": null, "urls": [], "raw_text": "Jason Baldridge and Geert-Jan Kruijff. 2003. Multi- Modal Combinatory Categorial Grammar. In Proceed- ings of EACL 10, pages 211-218.", "links": null }, "BIBREF3": { "ref_id": "b3", "title": "DotCCG and VisCCG: Wiki and Programming Paradigms for Improved Grammar Engineering with OpenCCG", "authors": [ { "first": "Jason", "middle": [], "last": "Baldridge", "suffix": "" }, { "first": "Sudipta", "middle": [], "last": "Chatterjee", "suffix": "" }, { "first": "Alexis", "middle": [], "last": "Palmer", "suffix": "" }, { "first": "Ben", "middle": [], "last": "Wing", "suffix": "" } ], "year": 2007, "venue": "Proceedings of GEAF", "volume": "", "issue": "", "pages": "", "other_ids": {}, "num": null, "urls": [], "raw_text": "Jason Baldridge, Sudipta Chatterjee, Alexis Palmer, and Ben Wing. 2007. DotCCG and VisCCG: Wiki and Programming Paradigms for Improved Grammar En- gineering with OpenCCG. In Proceedings of GEAF 2007.", "links": null }, "BIBREF4": { "ref_id": "b4", "title": "Lexically Specified Derivational Control in Combinatory Categorial Grammar", "authors": [ { "first": "Jason", "middle": [], "last": "Baldridge", "suffix": "" } ], "year": 2002, "venue": "", "volume": "", "issue": "", "pages": "", "other_ids": {}, "num": null, "urls": [], "raw_text": "Jason Baldridge. 2002. Lexically Specified Derivational Control in Combinatory Categorial Grammar. Ph.D. thesis, University of Edinburgh.", "links": null }, "BIBREF5": { "ref_id": "b5", "title": "Type-inheritance Combinatory Categorial Grammar", "authors": [ { "first": "John", "middle": [], "last": "Beavers", "suffix": "" } ], "year": 2004, "venue": "Proceedings of COLING-04", "volume": "", "issue": "", "pages": "", "other_ids": {}, "num": null, "urls": [], "raw_text": "John Beavers. 2004. Type-inheritance Combinatory Categorial Grammar. In Proceedings of COLING-04, Geneva, Switzerland.", "links": null }, "BIBREF6": { "ref_id": "b6", "title": "To Appear. Non-Transformational Syntax: A Guide to Current Models", "authors": [], "year": null, "venue": "", "volume": "", "issue": "", "pages": "", "other_ids": {}, "num": null, "urls": [], "raw_text": "Robert Borsley and Kersti B\u00f6rjars, editors. To Appear. Non-Transformational Syntax: A Guide to Current Models. Blackwell.", "links": null }, "BIBREF7": { "ref_id": "b7", "title": "Deriving the Predicate-Argument Structure for a Free Word Order Language", "authors": [ { "first": "Cem", "middle": [], "last": "Bozsahin", "suffix": "" } ], "year": 1998, "venue": "Proceedings of COLING-ACL '98", "volume": "", "issue": "", "pages": "", "other_ids": {}, "num": null, "urls": [], "raw_text": "Cem Bozsahin. 1998. Deriving the Predicate-Argument Structure for a Free Word Order Language. In Pro- ceedings of COLING-ACL '98.", "links": null }, "BIBREF8": { "ref_id": "b8", "title": "Wide-Coverage Efficient Statistical Parsing with CCG and Log-Linear Models", "authors": [ { "first": "Stephen", "middle": [], "last": "Clark", "suffix": "" }, { "first": "James", "middle": [], "last": "Curran", "suffix": "" } ], "year": 2007, "venue": "Computational Linguistics", "volume": "", "issue": "4", "pages": "", "other_ids": {}, "num": null, "urls": [], "raw_text": "Stephen Clark and James Curran. 2007. Wide-Coverage Efficient Statistical Parsing with CCG and Log-Linear Models. Computational Linguistics, 33(4).", "links": null }, "BIBREF9": { "ref_id": "b9", "title": "Combinatory Logic", "authors": [ { "first": "B", "middle": [], "last": "Haskell", "suffix": "" }, { "first": "Robert", "middle": [], "last": "Curry", "suffix": "" }, { "first": "", "middle": [], "last": "Feys", "suffix": "" } ], "year": 1958, "venue": "", "volume": "1", "issue": "", "pages": "", "other_ids": {}, "num": null, "urls": [], "raw_text": "Haskell B. Curry and Robert Feys. 1958. Combinatory Logic, volume 1. North Holland, Amsterdam.", "links": null }, "BIBREF10": { "ref_id": "b10", "title": "Efficient Normal-Form Parsing for Combinatory Categorial Grammars", "authors": [ { "first": "Jason", "middle": [], "last": "Eisner", "suffix": "" } ], "year": 1996, "venue": "Proceedings of the ACL 34", "volume": "", "issue": "", "pages": "", "other_ids": {}, "num": null, "urls": [], "raw_text": "Jason Eisner. 1996. Efficient Normal-Form Parsing for Combinatory Categorial Grammars. In Proceedings of the ACL 34.", "links": null }, "BIBREF11": { "ref_id": "b11", "title": "Aspects of the Spanish Causative Construction", "authors": [ { "first": "", "middle": [], "last": "Michael D Finnemann", "suffix": "" } ], "year": 1982, "venue": "", "volume": "", "issue": "", "pages": "", "other_ids": {}, "num": null, "urls": [], "raw_text": "Michael D Finnemann. 1982. Aspects of the Spanish Causative Construction. Ph.D. thesis, University of Minnesota.", "links": null }, "BIBREF12": { "ref_id": "b12", "title": "Logic, Language, and Meaning, volume II", "authors": [ { "first": "L", "middle": [ "T F" ], "last": "Gamut", "suffix": "" } ], "year": 1991, "venue": "", "volume": "", "issue": "", "pages": "", "other_ids": {}, "num": null, "urls": [], "raw_text": "L. T. F. Gamut. 1991. Logic, Language, and Meaning, volume II. Chicago University Press.", "links": null }, "BIBREF13": { "ref_id": "b13", "title": "Parsing and Derivational Equivalence", "authors": [ { "first": "Jeroen", "middle": [], "last": "Groenendijk", "suffix": "" }, { "first": "Martin", "middle": [], "last": "Stokhof", "suffix": "" } ], "year": 1989, "venue": "Handbook of Logic and Language, chapter 19", "volume": "", "issue": "", "pages": "1055--1124", "other_ids": {}, "num": null, "urls": [], "raw_text": "Jeroen Groenendijk and Martin Stokhof. 1997. Ques- tions. In Johan van Benthem and Alice ter Meulen, editors, Handbook of Logic and Language, chapter 19, pages 1055-1124. Elsevier Science, Amsterdam. Mark Hepple and Glyn Morrill. 1989. Parsing and Derivational Equivalence. In Proceedings of EACL 4.", "links": null }, "BIBREF14": { "ref_id": "b14", "title": "Generative Models for Statistical Parsing with Combinatory Categorial Grammar", "authors": [ { "first": "Julia", "middle": [], "last": "Hockenmaier", "suffix": "" }, { "first": "Mark", "middle": [], "last": "Steedman", "suffix": "" } ], "year": 2002, "venue": "Proceedings. of ACL 40", "volume": "", "issue": "", "pages": "335--342", "other_ids": {}, "num": null, "urls": [], "raw_text": "Julia Hockenmaier and Mark Steedman. 2002. Gen- erative Models for Statistical Parsing with Combina- tory Categorial Grammar. In Proceedings. of ACL 40, pages 335-342, Philadelpha, PA.", "links": null }, "BIBREF15": { "ref_id": "b15", "title": "Raising as Function Composition", "authors": [ { "first": "Pauline", "middle": [], "last": "Jacobson", "suffix": "" } ], "year": 1990, "venue": "Linguistics and Philosophy", "volume": "13", "issue": "", "pages": "423--475", "other_ids": {}, "num": null, "urls": [], "raw_text": "Pauline Jacobson. 1990. Raising as Function Composi- tion. Linguistics and Philosophy, 13:423-475.", "links": null }, "BIBREF16": { "ref_id": "b16", "title": "Towards a Variable-Free Semantics", "authors": [ { "first": "Pauline", "middle": [], "last": "Jacobson", "suffix": "" } ], "year": 1999, "venue": "Linguistics and Philosophy", "volume": "22", "issue": "", "pages": "117--184", "other_ids": {}, "num": null, "urls": [], "raw_text": "Pauline Jacobson. 1999. Towards a Variable-Free Se- mantics. Linguistics and Philosophy, 22:117-184.", "links": null }, "BIBREF17": { "ref_id": "b17", "title": "Radical Lexicalism", "authors": [ { "first": "Lauri", "middle": [], "last": "Karttunen", "suffix": "" } ], "year": 1989, "venue": "Alternative Conceptions of Phrase Structure", "volume": "", "issue": "", "pages": "", "other_ids": {}, "num": null, "urls": [], "raw_text": "Lauri Karttunen. 1989. Radical Lexicalism. In Mark Baltin and Anthony Kroch, editors, Alternative Con- ceptions of Phrase Structure. University of Chicago Press, Chicago.", "links": null }, "BIBREF18": { "ref_id": "b18", "title": "Incremental, Multi-Level Processing for Comprehending Situated Dialogue in Human-Robot Interaction", "authors": [ { "first": "Angelika", "middle": [], "last": "Kratzer", "suffix": "" }, { "first": ";", "middle": [], "last": "Geert-Jan", "suffix": "" }, { "first": "M", "middle": [], "last": "Kruijff", "suffix": "" }, { "first": "Pierre", "middle": [], "last": "Lison", "suffix": "" } ], "year": 1991, "venue": "Semantics: An International Handbook of Contemporary Semantic Research", "volume": "", "issue": "", "pages": "639--650", "other_ids": {}, "num": null, "urls": [], "raw_text": "Angelika Kratzer. 1991. Modality. In Arnim von Ste- chow and Dieter Wunderlich, editors, Semantics: An International Handbook of Contemporary Semantic Research, pages 639-650. Walter de Gruyter, Berlin. Geert-Jan M. Kruijff, Pierre Lison, Trevor Benjamin, Henrik Jacobsson, and Nick Hawes. 2007. Incremen- tal, Multi-Level Processing for Comprehending Situ- ated Dialogue in Human-Robot Interaction. In Lan- guage and Robots: Proceedings from the Symposium (LangRo'2007), Aveiro, Portugal.", "links": null }, "BIBREF19": { "ref_id": "b19", "title": "The mathematics of sentence structure", "authors": [ { "first": "Joachim", "middle": [], "last": "Lambek", "suffix": "" } ], "year": 1958, "venue": "American Mathematical Monthly", "volume": "65", "issue": "", "pages": "154--169", "other_ids": {}, "num": null, "urls": [], "raw_text": "Joachim Lambek. 1958. The mathematics of sentence structure. American Mathematical Monthly, 65:154- 169.", "links": null }, "BIBREF20": { "ref_id": "b20", "title": "Clitic Promotion and Mood in Spanish Verbal Complements", "authors": [ { "first": "Marta", "middle": [], "last": "Luj\u00e1n", "suffix": "" } ], "year": 1980, "venue": "Linguistics", "volume": "18", "issue": "", "pages": "381--484", "other_ids": {}, "num": null, "urls": [], "raw_text": "Marta Luj\u00e1n. 1980. Clitic Promotion and Mood in Span- ish Verbal Complements. Linguistics, 18:381-484.", "links": null }, "BIBREF21": { "ref_id": "b21", "title": "Categorial Type Logics", "authors": [ { "first": "Michael", "middle": [], "last": "Moortgat", "suffix": "" } ], "year": 1997, "venue": "Handbook of Logic and Language", "volume": "", "issue": "", "pages": "93--177", "other_ids": {}, "num": null, "urls": [], "raw_text": "Michael Moortgat. 1997. Categorial Type Logics. In Jo- han van Benthem and Alice ter Meulen, editors, Hand- book of Logic and Language, pages 93-177. North Holland, Amsterdam.", "links": null }, "BIBREF22": { "ref_id": "b22", "title": "To Appear. Multi-Modal Type Logical Grammar", "authors": [ { "first": "", "middle": [], "last": "Richard T Oehrle", "suffix": "" } ], "year": null, "venue": "Boersley and B\u00f6rjars (Borsley and B\u00f6rjars", "volume": "", "issue": "", "pages": "", "other_ids": {}, "num": null, "urls": [], "raw_text": "Richard T Oehrle. To Appear. Multi-Modal Type Log- ical Grammar. In Boersley and B\u00f6rjars (Borsley and B\u00f6rjars, To Appear).", "links": null }, "BIBREF23": { "ref_id": "b23", "title": "Dependency Categorial Grammar and Coordination", "authors": [ { "first": "Martin", "middle": [], "last": "Pickering", "suffix": "" }, { "first": "Guy", "middle": [], "last": "Barry", "suffix": "" } ], "year": 1993, "venue": "Linguistics", "volume": "31", "issue": "", "pages": "855--902", "other_ids": {}, "num": null, "urls": [], "raw_text": "Martin Pickering and Guy Barry. 1993. Dependency Categorial Grammar and Coordination. Linguistics, 31:855-902.", "links": null }, "BIBREF24": { "ref_id": "b24", "title": "Priming Effects in Combinatory Categorial Grammar", "authors": [ { "first": "David", "middle": [], "last": "Reitter", "suffix": "" }, { "first": "Julia", "middle": [], "last": "Hockenmaier", "suffix": "" }, { "first": "Frank", "middle": [], "last": "Keller", "suffix": "" } ], "year": 2006, "venue": "Proceedings of EMNLP-2006", "volume": "", "issue": "", "pages": "", "other_ids": {}, "num": null, "urls": [], "raw_text": "David Reitter, Julia Hockenmaier, and Frank Keller. 2006. Priming Effects in Combinatory Categorial Grammar. In Proceedings of EMNLP-2006.", "links": null }, "BIBREF25": { "ref_id": "b25", "title": "To Appear. Combinatory Categorial Grammar", "authors": [ { "first": "Mark", "middle": [], "last": "Steedman", "suffix": "" }, { "first": "Jason", "middle": [], "last": "Baldridge", "suffix": "" } ], "year": null, "venue": "Borsley and B\u00f6rjars (Borsley and B\u00f6rjars", "volume": "", "issue": "", "pages": "", "other_ids": {}, "num": null, "urls": [], "raw_text": "Mark Steedman and Jason Baldridge. To Appear. Com- binatory Categorial Grammar. In Borsley and B\u00f6rjars (Borsley and B\u00f6rjars, To Appear).", "links": null }, "BIBREF26": { "ref_id": "b26", "title": "Surface Structure and Interpretation", "authors": [ { "first": "Mark", "middle": [], "last": "Steedman", "suffix": "" } ], "year": 1996, "venue": "", "volume": "", "issue": "", "pages": "", "other_ids": {}, "num": null, "urls": [], "raw_text": "Mark Steedman. 1996. Surface Structure and Interpre- tation. MIT Press.", "links": null }, "BIBREF27": { "ref_id": "b27", "title": "The Syntactic Process", "authors": [ { "first": "Mark", "middle": [], "last": "Steedman", "suffix": "" } ], "year": 2000, "venue": "", "volume": "", "issue": "", "pages": "", "other_ids": {}, "num": null, "urls": [], "raw_text": "Mark Steedman. 2000. The Syntactic Process. MIT Press.", "links": null }, "BIBREF28": { "ref_id": "b28", "title": "Adapting Chart Realization to CCG", "authors": [ { "first": "Michael", "middle": [], "last": "White", "suffix": "" }, { "first": "Jason", "middle": [], "last": "Baldridge", "suffix": "" } ], "year": 2003, "venue": "Proceedings of ENLG", "volume": "", "issue": "", "pages": "", "other_ids": {}, "num": null, "urls": [], "raw_text": "Michael White and Jason Baldridge. 2003. Adapting Chart Realization to CCG. In Proceedings of ENLG.", "links": null }, "BIBREF29": { "ref_id": "b29", "title": "Efficient Realization of Coordinate Structures in Combinatory Categorial Grammar", "authors": [ { "first": "Michael", "middle": [], "last": "White", "suffix": "" } ], "year": 2006, "venue": "Research on Language and Computation", "volume": "4", "issue": "1", "pages": "39--75", "other_ids": {}, "num": null, "urls": [], "raw_text": "Michael White. 2006. Efficient Realization of Coordi- nate Structures in Combinatory Categorial Grammar. Research on Language and Computation, 4(1):39-75.", "links": null }, "BIBREF30": { "ref_id": "b30", "title": "Predictive Combinators: A Method for Efficient Processing of Combinatory Categorial Grammars", "authors": [ { "first": "Kent", "middle": [], "last": "Wittenburg", "suffix": "" } ], "year": 1987, "venue": "Proceedings of ACL 25", "volume": "", "issue": "", "pages": "", "other_ids": {}, "num": null, "urls": [], "raw_text": "Kent Wittenburg. 1987. Predictive Combinators: A Method for Efficient Processing of Combinatory Cat- egorial Grammars. In Proceedings of ACL 25.", "links": null }, "BIBREF31": { "ref_id": "b31", "title": "Online Learning of Relaxed CCG Grammars for Parsing to Logical Form", "authors": [ { "first": "Luke", "middle": [], "last": "Zettlemoyer", "suffix": "" }, { "first": "Michael", "middle": [], "last": "Collins", "suffix": "" } ], "year": 2007, "venue": "Proceedings of EMNLP-CoNLL", "volume": "", "issue": "", "pages": "", "other_ids": {}, "num": null, "urls": [], "raw_text": "Luke Zettlemoyer and Michael Collins. 2007. On- line Learning of Relaxed CCG Grammars for Parsing to Logical Form. In Proceedings of EMNLP-CoNLL 2007.", "links": null } }, "ref_entries": { "FIGREF0": { "type_str": "figure", "uris": null, "text": "10) . . . what you can and what you must not base your verdict on.", "num": null }, "FIGREF1": { "type_str": "figure", "uris": null, "text": "(19) There appear to have been [ neither [ any catastrophic consequences ], nor [ a drastic change in the average age of retirement ] ] .", "num": null }, "FIGREF2": { "type_str": "figure", "uris": null, "text": "Theorem 2 : If N F (\u03b1) and N F (\u03b1 ) are distinct parse trees, then their model-theoretic interpretations are distinct.", "num": null }, "TABREF3": { "text": ": \u03bbQ et ?yQy s/vp : \u03bbP et .P i s/s : \u03bbp t .\u2666p He made us read The Lord of the Rings.\"", "content": "
):
(21)whatIcan
s/(s/np) * * *>B * * *
3.3 The Spanish Causative Construction
The schema in (1) is also found in the widely-
studied Romance causative construction (Andrews
and Manning, 1999, a.m.o), illustrated in (22):
(22) NoshizoleerElSe\u00f1ordelosAnillos.
cl.1pmade.3sreadtheLordoftheRings
\"
", "type_str": "table", "html": null, "num": null } } } }