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Studia Logica

, Volume 103, Issue 3, pp 453–478 | Cite as

Lower Semilattice-Ordered Residuated Semigroups and Substructural Logics

  • Szabolcs MikulásEmail author
Article
  • 87 Downloads

Abstract

We look at lower semilattice-ordered residuated semigroups and, in particular, the representable ones, i.e., those that are isomorphic to algebras of binary relations. We will evaluate expressions (terms, sequents, equations, quasi-equations) in representable algebras and give finite axiomatizations for several notions of validity. These results will be applied in the context of substructural logics.

Keywords

Finite axiomatization Relation algebras Residuation Lambek calculus Relevance logics 

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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Department of Computer Science and Information Systems BirkbeckUniversity of LondonLondonUK

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