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Algebraic Models of Categorial Grammars

  • Wojciech Buszkowski

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.

Keywords

Algebraic Model Reduction System Algebraic Semantic Formal Grammar Categorial Grammar 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1985

Authors and Affiliations

  • Wojciech Buszkowski
    • 1
  1. 1.Institute of MathematicsAdam Mickiewicz UniversityPoznańPoland

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