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The attraction of Categorial Grammar (CG) as a notation for natural language grammar has always been the direct relation that it embodies between the syntax of a language and an applicative semantics. Common sense suggests that just such a relation should hold for natural languages, just as it does in the systems of logic which gave rise to CG in the first place. However, the existence of discontinuous constituents, extractions, and all the other phenomena whose importance was first and most clearly exposed by Chomsky (1957) makes it clear that something more is required than the basic ingredients of function and argument categories, plus functional application, prescribed by Ajdukiewicz (1935). Those who have attempted to cope with these phenomena within CG have proposed to "generalise' (Bach, 1983) or "extend' (Levin, 1982) the basic context-free apparatus by the addition of various operations on the functions and arguments, over and above simple functional application. These additions have included functional composition and type raising (Lambek, 1958, 1961; Geach, 1972), "wrapping' (Bach, 1979, 1980), and some others.

DOI: 10.1007/978-94-015-6878-4_15

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