Łukasiewicz logic: From proof systems to logic programming

George Metcalfe, Nicola Olivetti, Dov Gabbay

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


We present logic programming style "goal-directed" proof methods for Łukasiewicz logic Ł that both have a logical interpretation, and provide a suitable basis for implementation. We introduce a basic version, similar to goal-directed calculi for other logics, and make refinements to improve efficiency and obtain termination. We then provide an algorithm for fuzzy logic programming in Rational Pavelka logic RPL, an extension of Ł with rational constants.

Original languageEnglish
Pages (from-to)561-585
Number of pages25
JournalLogic Journal of the IGPL
Issue number5
StatePublished - Sep 2005
Externally publishedYes


  • Fuzzy logics
  • Goal-directed methods
  • Logic programming
  • Łukasiewicz logics


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