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First-order Nilpotent minimum logics: first steps

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Abstract

Inspired by the work done by Baaz et al. (Ann Pure Appl Log 147(1–2): 23–47, 2007; Lecture Notes in Computer Science, vol 4790/2007, pp 77–91, 2007) for first-order Gödel logics, we investigate Nilpotent Minimum logic NM. We study decidability and reciprocal inclusion of various sets of first-order tautologies of some subalgebras of the standard Nilpotent Minimum algebra, establishing also a connection between the validity in an NM-chain of certain first-order formulas and its order type. Furthermore, we analyze axiomatizability, undecidability and the monadic fragments.

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  1. Department of Mathematics “Federigo Enriques”, Università degli Studi di Milano, Via Saldini 50, 20133, Milano, Italy

    Matteo Bianchi

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Bianchi, M. First-order Nilpotent minimum logics: first steps. Arch. Math. Logic 52, 295–316 (2013). https://doi.org/10.1007/s00153-012-0317-4

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