Anaphora and Type Logical Grammar

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 Benthem1983pointsout)theCurry-Howardcorrespondence-acentral part of mathematical proof theory which establishes a deep connection betweenconstructivelogicsandthe?-calculus-suppliesthetypelogical 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.