Lower Semilattice-Ordered Residuated Semigroups and Substructural Logics
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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.
KeywordsFinite axiomatization Relation algebras Residuation Lambek calculus Relevance logics
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