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Monotone operators on Gödel logic

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Abstract

We consider an extension of Gödel logic by a unary operator that enables the addition of non-negative reals to truth-values. Although its propositional fragment has a simple proof system, first-order validity is Π 2-hard. We explain the close connection to Scarpellini’s result on Π 2-hardness of Łukasiewicz’s logic.

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Correspondence to Oliver Fasching.

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Supported in part by Austrian Science Fund (FWF): I-603 N18.

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Fasching, O., Baaz, M. Monotone operators on Gödel logic. Arch. Math. Logic 53, 261–284 (2014). https://doi.org/10.1007/s00153-013-0365-4

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  • DOI: https://doi.org/10.1007/s00153-013-0365-4

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