Representation of Residuated Semigroups in Some Algebras of Relations (The Method of Canonical Models)

Article type: Research Article

Authors: Buszkowski, Wojciech | Kołowska-Gawiejnowicz, Mirosława

Affiliations: Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Poznań Poland

Abstract: We prove some theorems on representation of residuated semigroups and monoids in algebras of binary relations. One of them has been proved in Andréka and Mikulás [3], and the others are new, though also closely related to some results in [3]. The main novelty of this paper is a simple method of proof, based upon a construction of canonical models for Lambek calculi by means of labeled formulas, whereas [3] uses graph-theoretic constructions. We handle labeled formulas in a way similar to Kurtonina [15] and the second author [14], but we make no use of Labeled Deductive Systems, which is an essential simplification.

DOI: 10.3233/FI-1997-3111

Journal: Fundamenta Informaticae, vol. 31, no. 1, pp. 1-12, 1997