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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 298 (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
The Grammar and Processing of Order and Dependency: a Categorial Approach
, 1990
"... This thesis presents accounts of a range of linguistic phenomena in an extended categorial framework, and develops proposals for processing grammars set within this framework. Linguistic phenomena whose treatment we address include word order, grammatical relations and obliqueness, extraction and is ..."
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Cited by 71 (6 self)
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This thesis presents accounts of a range of linguistic phenomena in an extended categorial framework, and develops proposals for processing grammars set within this framework. Linguistic phenomena whose treatment we address include word order, grammatical relations and obliqueness, extraction and island constraints, and binding. The work is set within a flexible categorial framework which is a version of the Lambek calculus (Lambek, 1958) extended by the inclusion of additional typeforming operators whose logical behaviour allows for the characterization of some aspect of linguistic phenomena. We begin with the treatment of extraction phenomena and island constraints. An account is developed in which there are many interrelated notions of boundary, and where the sensitivity of any syntactic process to a particular class of boundaries can be addressed within the grammar. We next present a new categorial treatment of word order which factors apart the specification of the order of a h...
Efficient NormalForm Parsing for Combinatory Categorial Grammar
 IN PROCEEDINGS OF THE 34TH MEETING OF THE ACL
, 1996
"... Under categorial grammars that have powerful rules like composition, a simple nword sentence can have exponentially many parses. Generating all parses is inefficient and obscures whatever true semantic ambiguities are in the input. This paper addresses the problem for a fairly general form of Combi ..."
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Cited by 60 (2 self)
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Under categorial grammars that have powerful rules like composition, a simple nword sentence can have exponentially many parses. Generating all parses is inefficient and obscures whatever true semantic ambiguities are in the input. This paper addresses the problem for a fairly general form of Combinatory Categorial Grammar, by means of an efficient, correct, and easy to implement normalform parsing technique. The parser
Multimodal Linguistic Inference
, 1995
"... In this paper we compare grammatical inference in the context of simple and of mixed Lambek systems. Simple Lambek systems are obtained by taking the logic of residuation for a family of multiplicative connectives =; ffl; n, together with a package of structural postulates characterizing the resourc ..."
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Cited by 51 (8 self)
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In this paper we compare grammatical inference in the context of simple and of mixed Lambek systems. Simple Lambek systems are obtained by taking the logic of residuation for a family of multiplicative connectives =; ffl; n, together with a package of structural postulates characterizing the resource management properties of the ffl connective. Different choices for Associativity and Commutativity yield the familiar logics NL, L, NLP, LP. Semantically, a simple Lambek system is a unimodal logic: the connectives get a Kripke style interpretation in terms of a single ternary accessibility relation modeling the notion of linguistic composition for each individual system. The simple systems each have their virtues in linguistic analysis. But none of them in isolation provides a basis for a full theory of grammar. In the second part of the paper, we consider two types of mixed Lambek systems. The first type is obtained by combining a number of unimodal systems into one multimodal logic. The...
Incremental processing and acceptability
 Computational Linguistics
, 2000
"... We describe a lefttoright incremental procedure for the processing of Lambek categorial grammar by proof net construction. A simple metric of complexity, the profile in time of the number of unresolved valencies, correctly predicts a wide variety of performance phenomena including garden pathing, ..."
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Cited by 30 (4 self)
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We describe a lefttoright incremental procedure for the processing of Lambek categorial grammar by proof net construction. A simple metric of complexity, the profile in time of the number of unresolved valencies, correctly predicts a wide variety of performance phenomena including garden pathing, the unacceptability of center embedding, preference for lower attachment, lefttoright quantifier scope preference, and heavy noun phrase shift.
Chart Parsing Lambek Grammars: Modal Extensions and Incrementality
, 1992
"... This paper describes a method for chart parsing Lam bek grammars. The method is of particular interest in two regards. FirsSly, it allows efficient processing of grammars which use necessity operators, an extension proposed for handling locality phenomena. Secondly, the method is emily adapted to ..."
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Cited by 20 (5 self)
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This paper describes a method for chart parsing Lam bek grammars. The method is of particular interest in two regards. FirsSly, it allows efficient processing of grammars which use necessity operators, an extension proposed for handling locality phenomena. Secondly, the method is emily adapted to allow incremental processing of Lambek grammars, a possibility that has hitherto been unavailable.
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 20 (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'...
A Hypothetical Reasoning Algorithm for Linguistic Analysis
 Journal of Logic and Computation
, 1994
"... The Lambek calculus, an intuitionistic fragment of Linear Logic, has recently been rediscovered by linguists. Due to its builtin hypothetical reasoning mechanism, it allows for describing a certain range of those phenomena in natural language syntax which involve incomplete subphrases or moved cons ..."
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Cited by 19 (2 self)
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The Lambek calculus, an intuitionistic fragment of Linear Logic, has recently been rediscovered by linguists. Due to its builtin hypothetical reasoning mechanism, it allows for describing a certain range of those phenomena in natural language syntax which involve incomplete subphrases or moved constituents. Previously, it seemed unclear how to extent traditional parsing techniques in order to incorporate reasoning about incomplete phrases, without causing the undesired effect of derivational equivalences. It turned out that the Lambek calculus offers a framework to formulate equivalent but more implementationoriented calculi where this problem does not occur. In this paper, such a theorem prover for the Lambek calculus, i.e. a parser for Lambek categorial grammars, is defined. Permutations of proof steps which would cause derivational equivalence in a purely sequential formulation do not play a role in a (pseudo)parallel approach which is based on a lemma table or a "chart". At 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 14 (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