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This monograph began life as a series of papers documenting five years of research into the logical foundations of Categorial Grammar, a grammatical paradigm which has close analogies with Lambda Calculus and Type Theory. The technical theory presented here stems from the interface between Logic and Linguistics and, in particular, the theory of generalized quantification. A categorical framework with lambda calculus-oriented semantics is a convenient vehicle for generalizing semantic insights (obtained in various corners of natural language) into one coherent theory. The book aims to dem

Mathematical logic --- Logic --- Philosophy of language --- Language and logic. --- Categorial grammar. --- Lambda calculus. --- Logic, Symbolic and mathematical. --- Mathematical linguistics. --- Algebraic linguistics --- Language and languages --- Linguistics --- Linguistics, Mathematical --- Applied linguistics --- Information theory --- Computational linguistics --- Algebra of logic --- Logic, Universal --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Calculus, Lambda --- Logic, Symbolic and mathematical --- Grammar, Categorial --- Grammar, Comparative and general --- Linguistics and logic --- Logic in language --- Semantics --- Statistical methods --- Mathematical models --- Philosophy --- Categorial grammar --- Lambda calculus --- Language and logic --- Mathematical linguistics --- Logic, symbolic and mathematical --- Grammaire catégorielle --- Lambda-calcul --- Langage et logique --- Logique symbolique et mathématique --- Linguistique mathématique --- Logic [Symbolic and mathematical ]