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 syntax-semantics 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

We present a system for generating parsers based directly on the metaphor of parsing as deduction. Parsing algorithms can be represented directly as deduction systems, and a single deduction engine can interpret such deduction systems so as to implement the corresponding parser. The method generalizes easily to parsers for augmented phrase structure formalisms, such as definiteclause grammars and other logic grammar formalisms, and has been used for rapid prototyping of parsing algorithms for a variety of formalisms including variants of tree-adjoining grammars, categorial grammars, and lexicalized context-free grammars.

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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 type-forming 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...

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this paper. Thanks are also due to Steve Pulman, Ewan Klein, David Beaver and Guy Barry for discussion during the early stages of the work, and to other members of the University of Edinburgh Centre for Cognitive Science and the University of Cambridge Computer Laboratory. The research was supported by the British Science and Engineering Research Council (Research Fellowship B/90/ITF/288, and Research Grant RR30718)

From a logical perspective, categorial type systems can be situated within a landscape of substructural logics --- logics with a structure-sensitive consequence relation. Research on these logics has shown that the inhabitants of the substructural hierarchy can be systematically related by embedding translations on the basis of structural modalities. The modal operators offer controlled access to stronger logics from within weaker ones by licensing of structural operations. Linguistic material exhibits structure in dimensions not covered by the standard structural rules. The purpose of this paper is to generalize the modalisation and licensing strategy to two such dimensions: phrasal structure and headedness. Phrasal domain-sensitive type systems capture the notion of constituent structure; constituency relaxation can be licensed via an associativity modality. The opposition between heads and non-heads introduces dependency structure, an autonomous dimension of linguistic structure wh...

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We describe a categorial system (PPTS) based on partial proof trees (PPTs) as the building blocks of the system. The PPTs are obtained by unfolding the arguments of the type that would be associated with a lexical item in a simple categorial grammar. The PPTs are the basic types in the system and a derivation proceeds by combining PPTs together. We describe the construction of the finite set of basic PPTs and the operations for combining them. PPTS can be viewed as a categorial system incorporating some of the key insights of lexicalized tree adjoining grammar, namely the notion of an extended domain of locality and the consequent factoring of recursion from the domain of dependencies. PPTS therefore inherits the linguistic and computational properties of that system, and so can be viewed as a `middle ground' between a categorial grammar and a phrase structure grammar. We also discuss the relationship between PPTS, natural deduction, and linear logic proof-nets, and argue that natural ...