The Complexity of 3-Valued Lukasiewicz Rules

Abstract

It is known that determining the satisfiability of n-valued Łukasiewicz rules is NP-complete for n ≥ 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. © Springer International Publishing Switzerland 2015.