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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 239 (5 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
TermLabeled Categorial Type Systems
 Linguistics and Philosophy
, 1994
"... Through language, we are able to assign symbolic analyses to linguistic entities physical objects and events whose complexity has no intrinsic upper bound. Such symbolic analyses are abstract, since a single physical entity can support distinct analyses. Yet we have partial intuitive access to the ..."
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Cited by 45 (0 self)
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Through language, we are able to assign symbolic analyses to linguistic entities physical objects and events whose complexity has no intrinsic upper bound. Such symbolic analyses are abstract, since a single physical entity can support distinct analyses. Yet we have partial intuitive access to the properties of these analyses through their projections in different 'dimensions', including the widely recognized and studied dimensions of phonology, syntax, and semantics/pragmatics. Each of these dimensions gives rise to a dimensionspecific problem of compositionality: given an analysis of a linguistic entity e, which has, for a specific dimension d the projection d(e), how do the global properties of d(e) depend on the correlative properties of the components of e, together with their mode of composition? But an additional question which we call the problem of generalized compositionality arises as well: how does composition in one dimension depend on composition in other dimensions? There are many possible answers to this question and existing grammatical architectures instantiate some of them. The question deserves to be stud
Generalized quantifiers and discontinuous type constructors
 In Arthur Horck and Wietske Sijtsma, editors, Discontinuous Constituency, Berlin. Mouton de Gruyter
, 1992
"... 1 A signbased categorial framework This paper investigates discontinuous type constructors within the framework of a signbased generalization of categorial type calculi. The paper takes its inspiration from Oehrle’s (1988) work on generalized compositionality for multidimensional linguistic objects ..."
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1 A signbased categorial framework This paper investigates discontinuous type constructors within the framework of a signbased generalization of categorial type calculi. The paper takes its inspiration from Oehrle’s (1988) work on generalized compositionality for multidimensional linguistic objects, and, we hope, may establish a bridge between work in Unification Categorial Grammar or HPSG, and the research that views categorial grammar from the perspective of substructural type logics. Categorial sequents are represented as composed of multidimensional signs, modelled as tuples of the form 〈Type, Semantics, Syntax〉 They simultaneously characterize the semantic and structural properties of linguistic objects in terms of a typeassignment labelled with semantic information (a lambda term) and structural, syntactic information. As argued elsewhere (Moortgat 1988), the structural information refers to phonological structuring of linguistic material, rather than to syntactic structure in the conventional sense. For the purposes of this paper, structural information is simplified to a string description.
A CompilationChart Method for Linear Categorial Deduction
, 1996
"... Recent work in categorial grammar has seen proposals for a wide range of systems, differing in their `resource sensitivity'... ..."
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Cited by 18 (5 self)
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Recent work in categorial grammar has seen proposals for a wide range of systems, differing in their `resource sensitivity'...
Categorial Formalisation of Relativisation: Pied Piping, Islands, and Extraction Sites
, 1992
"... ..."
Memoisation of Categorial Proof Nets: Parallelism in Categorial Processing
, 1996
"... We introduce a method of memoisation of categorial proof nets. Exploiting the planarity of noncommutative proof nets, and unifiability as a correctness criterion, parallelism is simulated through construction of a proof net matrix of most general unifiers for modules, in a manner analogous to the C ..."
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Cited by 16 (2 self)
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We introduce a method of memoisation of categorial proof nets. Exploiting the planarity of noncommutative proof nets, and unifiability as a correctness criterion, parallelism is simulated through construction of a proof net matrix of most general unifiers for modules, in a manner analogous to the CockeYoungerKasami algorithm for context free grammar. 1 Memoisation of categorial proof nets: parallelism in categorial processing 1 Introduction If the evolutionary tendency of grammatical formalisms could be summed up in one word, that word could well be lexicalism. The lexicon was once considered the locus of all and only idiosyncratic information; it may be hard now to find any proponents at all of such a view. Rather, one hears of the balance or tradeoff between lexicon and syntax: the tenet that the lexicon should comprise only what is idiosyncratic is, simply, no longer held. The notion that there is a compromise to be struck between lexicon and syntax is in turn rejected in the...
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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Cited by 13 (4 self)
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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
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 proving. The de ..."
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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...
Tuples, Discontinuity, and Gapping in Categorial Grammar
, 1993
"... This paper solves some puzzles in the formalisation of logic fo.r discontinuity in categorial grammax. A 'tuple' operation introduced in [Solias, 1992] is defined as a mode of prosodic combination which has associated projection functions, and consequently can support a property of unique prosodi ..."
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Cited by 11 (3 self)
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This paper solves some puzzles in the formalisation of logic fo.r discontinuity in categorial grammax. A 'tuple' operation introduced in [Solias, 1992] is defined as a mode of prosodic combination which has associated projection functions, and consequently can support a property of unique prosodic decomposability. Discontinuity operators are defined modeltheoretically by a residuation scheme which is paxticulaxly ammenable prooftheoretically. This enables a formulation which both improves on the logic for wrapping and infixing of [Moortgat, 1988] which is only partial, and resolves some problems of determinacy of insertion point in the application of these proposals to insitu binding phenomena. A discontinuous product is also defined by the residuation scheme, enabling formulation of rules of both use and proof for a 'substring' product that would have been similarly doomed to partial logic. We show
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, and one ..."
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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.