Abstract
Lambek logics are substructural logics related to the Syntactic Calculus of Lambek [17]. In this paper we prove several representation theorems for algebras of Lambek logics (residuated semigroups, residuated monoids and others) with respect to certain algebras of binary relations. First results of this kind were obtained by Andréka and Mikulás [1], using a method of labeled graphs. Other results were proved in [9,28], using a method of labeled formulas. In the present paper, we prove these and other results, using a construction of chains of partial representations; this idea was announced earlier in the abstract [5]. We also provide a simpler construction which works for right and left pregroups [8].
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Buszkowski, W. (2003). Relational Models of Lambek Logics. In: de Swart, H., Orłowska, E., Schmidt, G., Roubens, M. (eds) Theory and Applications of Relational Structures as Knowledge Instruments. Lecture Notes in Computer Science, vol 2929. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24615-2_9
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