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Lower Semilattice-Ordered Residuated Semigroups and Substructural Logics

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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.

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Authors and Affiliations

  1. Department of Computer Science and Information Systems Birkbeck, University of London, London, UK

    Szabolcs Mikulás

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  1. Szabolcs Mikulás
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Correspondence to Szabolcs Mikulás.

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In memoriam J. Lambek (1922–2014)

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Mikulás, S. Lower Semilattice-Ordered Residuated Semigroups and Substructural Logics. Stud Logica 103, 453–478 (2015). https://doi.org/10.1007/s11225-014-9574-z

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  • DOI: https://doi.org/10.1007/s11225-014-9574-z

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