Analytic Sequent Calculi for Abelian and Łukasiewicz Logics
In this paper we present the first labelled and unlabelled analytic sequent calculi for abelian logic A, the logic of lattice-ordered abelian groups with characteristic model ℤ, motivated in  as a logic of relevance and in  as a logic of comparison. We also show that the so-called material fragment of A coincides with Łukasiewicz’s infinite-valued logic Ł, hence giving us as a significant by-product, labelled and unlabelled analytic sequent calculi for Ł.
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