English

Sequent and Hypersequent Calculi for Abelian and Lukasiewicz Logics

Logic in Computer Science 2007-05-23 v1

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.

Keywords

Cite

@article{arxiv.cs/0211021,
  title  = {Sequent and Hypersequent Calculi for Abelian and Lukasiewicz Logics},
  author = {G. Metcalfe and N. Olivetti and D. Gabbay},
  journal= {arXiv preprint arXiv:cs/0211021},
  year   = {2007}
}

Comments

35 pages, 1 figure

R2 v1 2026-07-22T12:20:23.764Z