Analytic Sequent Calculi for Abelian and Łukasiewicz Logics

  • George Metcalfe
  • Nicola Olivetti
  • Dov Gabbay
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2381)


In this paper we present the first labelled and unlabelled analytic sequent calculi for abelian logic A, the logic of lattice-ordered abelian groups with characteristic model ℤ, motivated in [10] as a logic of relevance and in [3] as a logic of comparison. We also show that the so-called material fragment of A coincides with Łukasiewicz’s infinite-valued logic Ł, hence giving us as a significant by-product, labelled and unlabelled analytic sequent calculi for Ł.


Propositional Variable Proof Theory Sequent Calculus Labelling Function Label Sequent 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • George Metcalfe
    • 1
  • Nicola Olivetti
    • 2
  • Dov Gabbay
    • 1
  1. 1.Department of Computer ScienceKing’s College LondonLondonUK
  2. 2.Department of Computer ScienceUniversity of TurinTurinItaly

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