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Sequent and Hypersequent Calculi for Abelian and Lukasiewicz Logics

G. Metcalfe·N. Olivetti·D. Gabbay
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Abstract

We present two embeddings of infinite-valued Lukasiewicz logic L into Meyer and Slaney's abelian logic A, the logic of lattice-ordered abelian groups. We give new analytic proof systems for A and use the embeddings to derive corresponding systems for L. These include: hypersequent calculi for A and L and terminating versions of these calculi; labelled single sequent calculi for A and L of complexity co-NP; unlabelled single sequent calculi for A and L.

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G. Metcalfe, N. Olivetti, D. Gabbay. 2002-11-18. Sequent and Hypersequent Calculi for Abelian and Lukasiewicz Logics. https://arxiv.org/abs/cs/0211021

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