Page 338 - Encyclopedia of Philosophy of Language

Formal Semantics
A\B and B/A with the type (rfpE(A),TfPE(B)). [/L] and [\L] correspond to 'application,' [/R] and [\R] to 'abstraction,' and [Ax] and [Cut] to 'identity':
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As for the relationship between categories and types, Montague's semantics and categorial grammar under- went a parallel development. In AB grammars, each expression is assigned exactly one category. L is far more flexible; the presence of theorems like raising (cf. above) entails that an expression belongs to an infinite number of syntactic categories, and its interpretations in those categories to an infinite number of semantic types. This increased syntactic/semantic flexibility mirrors (but can be distinguished from) the purely semantic flexibility argued for within Montague gram- mar. In conjunction with additional lexical poly- morphism, categorial flexibility has been successfully exploited in categorial accounts of nonconstituent coordination, scope ambiguities, negative polarity, and other linguistic phenomena.
Research within categorial grammar has headed towards the incorporation of new type-forming oper- ators, to be used for the description of extraction, gapping, locality facts, etc. In this area, work on linear logic (cf. Girard 1987), of which L turned out to be a weak, noncommutative implicational fragment, has proved to be a valuable heuristic tool.
See also: Categorial Grammar; Montague Grammar. Bibliography
Ajdukiewicz K 1935 Die syntaktische Konnexitat. Studio Philosophica 1: 1-27
The de dietoIde re distinction is a classification usually effected on sentences which contain 'modal' contexts (e.g., it is possible that or a subjunctive verb) or 'epi-
stemic' contexts (Ralph believes that or it is a priori thai). For some it is primarily a syntactic classification and for others primarily a semantic one, and one
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De Dicto/De Re G.Forbes