SAT in Monadic Gödel Logics: A Borderline between Decidability and Undecidability

Authors:
Matthias Baaz;Agata Ciabattoni;Norbert Preining
Affiliations:
Technische Universität Wien, Austria;Technische Universität Wien, Austria;Technische Universität Wien, Austria
Venue:
WoLLIC '09 Proceedings of the 16th International Workshop on Logic, Language, Information and Computation
Year:
2009

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Abstract

We investigate satisfiability in the monadic fragment of first-order Gädel logics. These are a family of finite- and infinite-valued 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.