The Complexity of 3-Valued Łukasiewicz Rules

  • Miquel BofillEmail author
  • Felip Manyà
  • Amanda Vidal
  • Mateu Villaret
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9321)


It is known that determining the satisfiability of n-valued Łukasiewicz rules is NP-complete for \(n \ge 4\), as well as that it can be solved in time linear in the length of the formula in the Boolean case (when \(n=2\)). However, the complexity for \(n=3\) is an open problem. In this paper we formally prove that the satisfiability problem for 3-valued Łukasiewicz rules is NP-complete. Moreover, we also prove that when the consequent of the rule has at most one element, the problem is polynomially solvable.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Miquel Bofill
    • 1
    Email author
  • Felip Manyà
    • 2
  • Amanda Vidal
    • 2
  • Mateu Villaret
    • 1
  1. 1.Universitat de GironaGironaSpain
  2. 2.Artificial Intelligence Research Institute (IIIA, CSIC)BellaterraSpain

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