Sequent and hypersequent calculi for Abelian and Łukasiewicz logics

George Metcalfe, Nicola Olivetti, Dov Gabbay

Research output: Contribution to journalArticlepeer-review

41 Scopus citations


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 languageEnglish
Pages (from-to)578-613
Number of pages36
JournalACM Transactions on Computational Logic
Issue number3
StatePublished - Jul 2005
Externally publishedYes


  • Abelian logic
  • Hypersequents
  • Sequents
  • ŁUkasiewicz logic


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