Derived Tree Languages of Nonassociative Lambek Categorial Grammars with Product

Article type: Research Article

Authors: Kandulski, Maciej

Affiliations: Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 85, 61-614 Poznań, Poland

Abstract: We introduce the notion of derived tree corresponding with a derivation in the nonassociative Lambek calculus with product, and examine languages of derived trees determined by categorial grammars employing the calculus as a type reduction system. We prove that the class of derived tree languages of nonassociative Lambek grammars with product contains only regular tree languages.

Keywords: Categorial grammars, Lambek calculus, derived tree languages

Journal: Fundamenta Informaticae, vol. 55, no. 3-4, pp. 349-362, 2003