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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.
List of Tables. Preface. Acknowledgments. 1. TYPE LOGICAL GRAMMAR: THE FRAMEWORK. 1 Basic Categorial Grammar. 2 Combinators and Type Logical Grammar. 3 Historical and bibliographical remarks. 2. THE PROBLEM OF ANAPHORA. 1 Anaphora and semantic resource sensitivity. 2 Variables in TLG. 3 Previous Categorial approaches to anaphora. 4 Summary. 3. LAMBEK CALCULUS WITH LIMITED CONTRACTION. 1 The agenda. 2 Contraction? 3 The Logic LLC. 4 Relation to Jacobson's system. 4. PRONOUNS AND QUANTIFICATION. 1 Basic cases. 2 Binding by wh -operators. 3 Binding by quantifiers. 4 Weak crossover. 5 Precedence versus c-command. 6 Backward binding and reconstruction. 5. VERB PHRASE ELLIPSIS. 1 Introduction. 2 VPE: The basic idea. 3 Interaction with pronominal anaphora. 4 Interaction of VPE and quantification. 5 VPE and Polymorphism. 6 Parallelism versus source ambiguity. 6. INDEFINITES. 1 Introduction. 2 Dekker's Predicate Logic with Anaphora. 3 Bringing PLA into TLG. 4 Donkey sentences. 5 Indefinites and scope. 6 Sluicing. 7 Summary and desiderata. References. Index.