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.
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