Analytic calculi for product logics

George Metcalfe, Nicola Olivetti, Dov Gabbay

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


Product logic Π is an important t-norm based fuzzy logic with conjunction interpreted as multiplication on the real unit interval [0,1], while Cancellative hoop logic CHL is a related logic with connectives interpreted as for Π but on the real unit interval with 0 removed (0,1]. Here we present several analytic proof systems for Π and CHL, including hypersequent calculi, co-NP labelled calculi and sequent calculi.

Original languageEnglish
Pages (from-to)859-889
Number of pages31
JournalArchive for Mathematical Logic
Issue number7
StatePublished - Oct 2004
Externally publishedYes


  • Fuzzy logic
  • Hypersequent calculi
  • Product logic
  • Sequent calculi


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