Sequent and hypersequent calculi for Abelian and Łukasiewicz logics

George Metcalfe; Nicola Olivetti; Dov Gabbay

doi:10.1145/1071596.1071600

Sequent and hypersequent calculi for Abelian and Łukasiewicz logics

George Metcalfe
, Nicola Olivetti
, Dov Gabbay

King's College London
University of Turin

Research output: Contribution to journal › Article › peer-review

49 Scopus citations

Abstract

We present two embeddings of Łukasiewicz logic Ł 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 Ł. These include hypersequent calculi, terminating hypersequent calculi, co-NP labeled sequent calculi, and unlabeled sequent calculi.

Original language	English
Pages (from-to)	578-613
Number of pages	36
Journal	ACM Transactions on Computational Logic
Volume	6
Issue number	3
DOIs	https://doi.org/10.1145/1071596.1071600
State	Published - Jul 2005
Externally published	Yes

Keywords

Abelian logic
Hypersequents
Sequents
ŁUkasiewicz logic

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10.1145/1071596.1071600

Cite this

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KW - ŁUkasiewicz logic

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Sequent and hypersequent calculi for Abelian and Łukasiewicz logics

Abstract

Keywords

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