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 Type Logical Grammar
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.