Abstract
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 [10] as a logic of relevance and in [3] 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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Metcalfe, G., Olivetti, N., Gabbay, D. (2002). Analytic Sequent Calculi for Abelian and Łukasiewicz Logics. In: Egly, U., Fermüller, C.G. (eds) Automated Reasoning with Analytic Tableaux and Related Methods. TABLEAUX 2002. Lecture Notes in Computer Science(), vol 2381. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45616-3_14
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DOI: https://doi.org/10.1007/3-540-45616-3_14
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