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Lower Semilattice-Ordered Residuated Semigroups and Substructural Logics
Studia Logica 103 (3):453-478 (2015)
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 in representable algebras and give finite axiomatizations for several notions of validity. These results will be applied in the context of substructural logicsOther Versions
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References found in this work
The Mathematics of Sentence Structure.Joachim Lambek - 1958 - Journal of Symbolic Logic 65 (3):154-170.
The Semantics of Entailment.Richard Routley & Robert K. Meyer - 1973 - In Hugues Leblanc (ed.), Truth, Syntax, and Modality: Proceedings Of The Temple University Conference On Alternative Semantlcs. Amsterdam and London: North-Holland Publishing Company. pp. 199-243.
The Semantics of Entailment.Richard Routley & Robert K. Meyer - 1977 - Journal of Symbolic Logic 42 (2):315-316.
Relevance logic and the calculus of relations.Roger D. Maddux - 2010 - Review of Symbolic Logic 3 (1):41-70.
Relevance logics and relation algebras.Katalin Bimbó, J. Michael Dunn & Roger D. Maddux - 2009 - Review of Symbolic Logic 2 (1):102-131.
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