Sequent and Hypersequent Calculi for Abelian and Lukasiewicz Logics

Details Sequent and Hypersequent Calculi for Abelian and Lukasiewicz Logics Sequent and Hypersequent Calculi for Abelian and Lukasiewicz Logics

2002-11-18

arxiv.org/abs/cs/0211021v1

Computer Science

Logic in Computer Science

35 pages, 1 figure

Scientific paper

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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