Type Logical Grammar is a framework that emerged from the synthesis of two traditions: Categorial Grammar from formal linguistics and substructural logics from logic. Grammatical composition is conceived as resource conscious logical deduction. Such a grammar is necessarily surface oriented and lexicalistic. The Curry-Howard correspondence supplies an elegant compositional mapping from syntax to semantics.

Anaphora does not seem to fit well into this framework. In type logical deductions, each resource is used exactly once. Anaphora, however, is a phenomenon where semantic resources are used more than once. Generally admitting the multiple use of lexical resources is not possible because it would lead to empirical inadequacy and computational intractability.

This book develops a hybrid architecture that allows to incorporate anaphora resolution into grammatical deduction while avoiding these consequences. To this end, the grammar logic is enriched with a connective that specifically deals with anaphora.

After giving a self-contained introduction into Type Logical Grammar in general, the book discusses the formal properties of this connective. In the sequel, Jäger applies this machinery to numerous linguistic phenomena pertaining to the interaction of pronominal anaphora, VP ellipsis and quantification. In the final chapter, the framework is extended to indefiniteness, specificity and sluicing.

Zusammenfassung
ThisbookdiscusseshowTypeLogicalGrammarcanbemodi?edinsuch awaythatasystematictreatmentofanaphoraphenomenabecomesp- sible without giving up the general architecture of this framework. By Type Logical Grammar, I mean the version of Categorial Grammar that arose out of the work of Lambek, 1958 and Lambek, 1961. There Ca- gorial types are analyzed as formulae of a logical calculus. In particular, the Categorial slashes are interpreted as forms of constructive impli- tion in the sense of Intuitionistic Logic. Such a theory of grammar is per se attractive for a formal linguist who is interested in the interplay between formal logic and the structure of language. What makes L- bekstyleCategorialGrammarevenmoreexcitingisthefactthat(asvan Benthem,1983pointsout)theCurry-Howardcorrespondenceacentral part of mathematical proof theory which establishes a deep connection betweenconstructivelogicsandthe?-calculussuppliesthetypelogical syntax with an extremely elegant and independently motivated interface to model-theoretic semantics. Prima facie, anaphora does not ?t very well into the Categorial picture of the syntax-semantics interface. The Curry-Howard based composition of meaning operates in a local way, and meaning ass- bly is linear, i.e., every piece of lexical meaning is used exactly once. Anaphora, on the other hand, is in principle unbounded, and it involves by de?nition the multiple use of certain semantic resources. The latter problem has been tackled by several Categorial grammarians by ass- ing su?ciently complex lexical meanings for anaphoric expressions, but the locality problem is not easy to solve in a purely lexical way.

Inhalt

List of Tables. Preface. Acknowledgments. Type Logical Grammar: The Framework. Basic Categorial Grammar. Combinators and Type Logical Grammar. Historical and bibliographical remarks.- The Problem of Anaphora. Anaphora and semantic resource sensitivity. Variables in TLG. Previous Categorial approaches to anaphora. Summary.- Lambek Calculus with Limited Contraction. The agenda. Contraction? The Logic LLC. Relation to Jacobson's system.- Pronouns and Quantification. Basic cases. Binding by wh-operators. Binding by quantifiers. Weak crossover. Precedence versus c-command. Backward binding and reconstruction.- Verb Phrase Ellipsis. Introduction. VPE: The basic idea. Interaction with pronominal anaphora. Interaction of VPE and quantification. VPE and Polymorphism. Parallelism versus source ambiguity.- Indefinites. Introduction. Dekker's Predicate Logic with Anaphora. ringing PLA into TLG. Donkey sentences. Indefinites and scope. Sluicing. Summary and desiderata.- References. Index.