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SAT in Monadic Gödel Logics: a borderline between decidability and undecidability
"... Abstract. We investigate satisfiability in the monadic fragment of firstorder Gödel logics. These are a family of finite and infinitevalued logics where the sets of truth values V are closed subsets of [0, 1] containing 0 and 1. We identify conditions on the topological type of V that determine th ..."
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Abstract. We investigate satisfiability in the monadic fragment of firstorder Gödel logics. These are a family of finite and infinitevalued logics where the sets of truth values V are closed subsets of [0, 1] containing 0 and 1. We identify conditions on the topological type of V that determine the decidability or undecidability of their satisfiability problem. 1
Firstorder satisfiability in Gödel logics: an NPcomplete fragment
, 2011
"... Defined over sets of truth values V which are closed subsets of [0, 1] containing both 0 and 1, Gödel logics GV are prominent examples of manyvalued logics. We investigate a firstorder fragment of GV extended with ∆ that is powerful enough to formalize important properties of fuzzy rulebased syst ..."
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Defined over sets of truth values V which are closed subsets of [0, 1] containing both 0 and 1, Gödel logics GV are prominent examples of manyvalued logics. We investigate a firstorder fragment of GV extended with ∆ that is powerful enough to formalize important properties of fuzzy rulebased systems. The satisfiability problem in this fragment is shown to be NPcomplete for all GV, also in presence of an additional, involutive, negation. In contrast to the onevariable case, in the considered fragment only two infinitevalued Gödel logics extended with ∆ differ w.r.t. satisfiability. Only one of them enjoys the finite model property.