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Categorial Type Logics
 Handbook of Logic and Language
, 1997
"... Contents 1 Introduction: grammatical reasoning 1 2 Linguistic inference: the Lambek systems 5 2.1 Modelinggrammaticalcomposition ............................ 5 2.2 Gentzen calculus, cut elimination and decidability . . . . . . . . . . . . . . . . . . . . 9 2.3 Discussion: options for resource mana ..."
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Cited by 299 (6 self)
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Contents 1 Introduction: grammatical reasoning 1 2 Linguistic inference: the Lambek systems 5 2.1 Modelinggrammaticalcomposition ............................ 5 2.2 Gentzen calculus, cut elimination and decidability . . . . . . . . . . . . . . . . . . . . 9 2.3 Discussion: options for resource management . . . . . . . . . . . . . . . . . . . . . . 13 3 The syntaxsemantics interface: proofs and readings 16 3.1 Term assignment for categorial deductions . . . . . . . . . . . . . . . . . . . . . . . . 17 3.2 Natural language interpretation: the deductive view . . . . . . . . . . . . . . . . . . . 21 4 Grammatical composition: multimodal systems 26 4.1 Mixedinference:themodesofcomposition........................ 26 4.2 Grammaticalcomposition:unaryoperations ....................... 30 4.2.1 Unary connectives: logic and structure . . . . . . . . . . . . . . . . . . . . . . . 31 4.2.2 Applications: imposing constraints, structural relaxation
LambdaGrammars and the SyntaxSemantics Interface
, 2001
"... types in this paper are built up from ground types s, np and n with the help of implication, and thus have forms such as np s, n((np s)s), etc. A restriction on signs is that a sign of abstract type A should have a term of type A in its ith dimension. The values of the function : for ground t ..."
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Cited by 22 (2 self)
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types in this paper are built up from ground types s, np and n with the help of implication, and thus have forms such as np s, n((np s)s), etc. A restriction on signs is that a sign of abstract type A should have a term of type A in its ith dimension. The values of the function : for ground types can be chosen on a per grammar basis and in this paper are as in Table 2. For complex types, the rule is that (AB) = A B . This means, for example, that np(np s) = np(np s) = (t)((t)t) and that np(np s) = e(e(st)). As a consequence, (2c) should be of type np(np s). Similarly, (2a) and (2b) can be taken to be of type np, (3a) and (3b) are of types np s and s respectively, etc. In general, if M has abstract type AB and N abstract type A, then the pointwise application M(N) is de ned and has type B.
On the expressive power of abstract categorial grammars: Representing contextfree formalisms
 Journal of Logic, Language and Information
, 2004
"... Abstract. We show how to encode contextfree string grammars, linear contextfree tree grammars, and linear contextfree rewriting systems as Abstract Categorial Grammars. These three encodings share the same constructs, the only difference being the interpretation of the composition of the productio ..."
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Cited by 21 (5 self)
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Abstract. We show how to encode contextfree string grammars, linear contextfree tree grammars, and linear contextfree rewriting systems as Abstract Categorial Grammars. These three encodings share the same constructs, the only difference being the interpretation of the composition of the production rules. It is interpreted as a firstorder operation in the case of contextfree string grammars, as a secondorder operation in the case of linear contextfree tree grammars, and as a thirdorder operation in the case of linear contextfree rewriting systems. This suggest the possibility of defining an Abstract Categorial Hierarchy. 1.
Alternating Quantifier Scope in CCG
, 1999
"... The paper shows that movement or equivalent computational structurechanging operations of any kind at the level of logical form can be dispensed with entirely in capturing quantifier scope ambiguity. It offers a new semantics whereby the effects of quantifier scope alternation can be obtained by an ..."
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Cited by 15 (0 self)
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The paper shows that movement or equivalent computational structurechanging operations of any kind at the level of logical form can be dispensed with entirely in capturing quantifier scope ambiguity. It offers a new semantics whereby the effects of quantifier scope alternation can be obtained by an entirely monotonic derivation, without typechanging rules. The paper follows Fodor (1982), Fodor and Sag (1982), and Park (1995, 1996) in viewing many apparent scope ambiguities as arising from referential categories rather than true generalized quantifiers.
A categorial framework for composition in multiple linguistic domains
 In Proceedings of the 4th International Conference on Cognitive Science of Natural Language Processing
, 1995
"... We describe a computational framework for a grammar architecture in which different linguistic domains such as morphology, syntax, and semantics are treated not as separate components but compositional domains. Word and phrase formation are modeled as uniform processes contributing to the derivation ..."
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Cited by 14 (7 self)
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We describe a computational framework for a grammar architecture in which different linguistic domains such as morphology, syntax, and semantics are treated not as separate components but compositional domains. Word and phrase formation are modeled as uniform processes contributing to the derivation of the semantic form. The morpheme, as well as the lexeme, has lexical representation in the form of semantic content, tactical constraints, and phonological realization. The model is based on Combinatory Categorial Grammars. 1
HigherOrder Linear Logic Programming of Categorial Deduction’, Report de Recerca LSI–94–42–R, Departament de Llenguatges i
 Sistemes Informàtics, Universitat Politècnica de Catalunya Morrill, Glyn: 1994b, Type Logical Grammar: Categorial Logic of Signs
"... We show how categorial deduction can be implemented in higherorder (linear) logic programming, thereby realising parsing as deduction for the associative and nonassociative Lambek calculi. This provides a method of solution to the parsing problem of Lambek categorial grammar applicable to a variet ..."
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We show how categorial deduction can be implemented in higherorder (linear) logic programming, thereby realising parsing as deduction for the associative and nonassociative Lambek calculi. This provides a method of solution to the parsing problem of Lambek categorial grammar applicable to a variety of its extensions. The present work deals with the parsing problem for Lambek calculus and its extensions as developed
Language, Lambdas, and Logic
 Resource Sensitivity in Binding and Anaphora
, 2003
"... Categorial Grammars'. Section 4 then continues with a closer look at possible ways to set up a particular Lambda Grammar, lling in some design choices. In particular we will opt for a three dimensional grammar there; one component will deal with dominance and precedence, one with semantics, an ..."
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Categorial Grammars'. Section 4 then continues with a closer look at possible ways to set up a particular Lambda Grammar, lling in some design choices. In particular we will opt for a three dimensional grammar there; one component will deal with dominance and precedence, one with semantics, and one with syntactic features. These choices bring us in close contact with the traditional architecture of LexicalFunctional Grammar (LFG, (Kaplan and Bresnan 1982), for further connections with LFG see (Oehrle 1999) and (Muskens 2001a), which is based upon the present system) and indeed the LFG architecture inspires our answer to question 4 above. Section 4 also works out the logics of the three grammatical components in some detail and thus illustrates one possible set of answers to question 3. For the semantic component we choose a standard type logic with possible worlds; for the feature component a type logic over the rstorder theory of features ((Johnson 1991)); and the multimodal approach to grammar that is found in most modern versions of the Lambek Calculus (see (Moortgat 1997) and references therein) will serve as a basis of the component dealing with dominance and precedence. The multimodal approach is thus moved from the general level of combing signs to one of the special dimensions of the grammar, another illustration of the modularity of the setup. The chapter ends with a short conclusion.
Clausal Proofs and Discontinuity
, 1995
"... We consider the task of theorem proving in Lambek calculi and their generalisation to "multimodal residuation calculi". These form an integral part of categorial logic, a logic of signs stemming from categorial grammar, on the basis of which language processing is essentially theorem provi ..."
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Cited by 11 (3 self)
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We consider the task of theorem proving in Lambek calculi and their generalisation to "multimodal residuation calculi". These form an integral part of categorial logic, a logic of signs stemming from categorial grammar, on the basis of which language processing is essentially theorem proving. The demand of this application is not just for efficient processing of some or other specific calculus, but for methods that will be generally applicable to categorial logics. It is proposed that multimodal cases be treated by dealing with the highest common factor of all the connectives as linear (propositional) validity. The prosodic (sublinear) aspects are encoded in labels, in effect the termstructure of quantified linear logic. The correctness condition on proof nets ("long trip condition") can be implemented by SLD resolution in linear logic with unification on labels/terms limited to one way matching. A suitable unification strategy is obtained for calculi of discontinuity by normalisation...
Hyperintensional Dynamic Semantics ⋆ Analyzing Definiteness with Enriched Contexts
"... Abstract. We present a dynamic semantic theory formalized in higher order logic that synthesizes aspects of de Groote’s continuationbased dynamics and Pollard’s hyperintensional semantics. In this theory, we rely on an enriched notion of discourse context inspired by the work of Heim and Roberts. W ..."
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Cited by 8 (5 self)
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Abstract. We present a dynamic semantic theory formalized in higher order logic that synthesizes aspects of de Groote’s continuationbased dynamics and Pollard’s hyperintensional semantics. In this theory, we rely on an enriched notion of discourse context inspired by the work of Heim and Roberts. We show how to use this enriched context to improve on de Groote’s treatment of English definite anaphora by modeling it as presupposition fulfillment.
Categorial Grammar and LexicalFunctional Grammar
 Proceedings of the LFG01 Conference, University of Hong Kong, CSLI Publications, Stanford CA
, 2001
"... This paper introduces grammar, a form of categorial grammar that has much in common with LFG. Like other forms of categorial grammar, grammars are multidimensional and their components are combined in a strictly parallel fashion. Grammatical representations are combined with the help of linear ..."
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Cited by 8 (3 self)
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This paper introduces grammar, a form of categorial grammar that has much in common with LFG. Like other forms of categorial grammar, grammars are multidimensional and their components are combined in a strictly parallel fashion. Grammatical representations are combined with the help of linear combinators, closed pure terms in which each abstractor binds exactly one variable. Mathematically this is equivalent to employing linear logic, in use in LFG for semantic composition, but the method seems more practicable. While grammars could be used to formalize many approaches to grammatical theory, they are certainly natural as a basis for the formalization of LFG. This leads to a theory I would like to call LFG. In this paper it will be shown how the standard components of LFG can be set up in the framework. We will have descriptions of cstructure, descriptions of fstructure, and semantics. The dierence between dening and constraining information will be explained in terms of entailment, and requirements on longdistance paths in fstructure will be explained in terms of entailment in the presence of a simple set of axioms.