Abstract
Categorial grammars (the term introduced by Bar Hillel et al. (1960)) are the formal grammars which comprise two basic constituents: (1) an initial type assignment, i.e., a function which assigns a finite set of syntactic types to each atomic expression (word) of a given language, (2) a system of type reduction laws which enables one to produce the terminal type assignment, i.e., a function which assigns a set of syntactic types to each expression of that language (cf. Marcus (1967)). The types are intended to denote syntactic categories of expressions (we identify the categories with sets of expressions), and the type reduction laws reflect certain universal (that means, independent of a particular language) relations between categories. The very idea of categorial grammar should be credited to Ajdukiewicz (1935), though, of course, some origins can be traced back to Frege, Leśniewski, Tarski and others.
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Buszkowski, W. (1985). Algebraic Models of Categorial Grammars. In: Dorn, G., Weingartner, P. (eds) Foundations of Logic and Linguistics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-0548-2_18
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DOI: https://doi.org/10.1007/978-1-4899-0548-2_18
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