Abstract
The monadic fragments of first-order Gödel logics are investigated. It is shown that all finite-valued monadic Gödel logics are decidable; whereas, with the possible exception of one (G↑), all infinite-valued monadic Gödel logics are undecidable. For the missing case G↑ the decidability of an important sub-case, that is well motivated also from an application oriented point of view, is proven. A tight bound for the cardinality of finite models that have to be checked to guarantee validity is extracted from the proof. Moreover, monadic G↑, like all other infinite-valued logics, is shown to be undecidable if the projection operator Δ is added, while all finite-valued monadic Gödel logics remain decidable with Δ.
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Baaz, M., Ciabattoni, A., Fermüller, C.G. (2007). Monadic Fragments of Gödel Logics: Decidability and Undecidability Results. In: Dershowitz, N., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2007. Lecture Notes in Computer Science(), vol 4790. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75560-9_8
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