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In categorial grammar, expressions are classified by structured types. The set of types is the recursive closure of a set of atomic types under a number of type-constructors, so that types are algebraic terms like arithmetic expressions or logical formulas. The rules of categorical grammar are supposed to express the laws obeyed by the types according to the ‘meaning’ of the type-constructors. A set of such rules forms a deductive system or logical calculus. A categorial grammar consists of a system of types, a calculus for those types, and a lexicon that is an assignment of types to basic expressions. The language thereby defined consists of the expressions derivable from the lexicon by the calculus. In the purest form of categorial grammar, the calculus would express all and only the laws of the types, and would be universal. This chapter discusses the following: Lambek calculus, basic discontinuous Lambek calculus, syntactic structures as proof nets, categorial semantics, and quantifier scoping and quantifier scope preference.

*Keywords: *
categorial grammar;
calculus;
Lambek calculus;
syntactic structures;
semantics;
quantifier scoping

*Article.*
*4620 words.*

*Subjects: *
Linguistics
;
Grammar, Syntax and Morphology
;
Semantics

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