First-order Nilpotent minimum logics: first steps

Archive for Mathematical Logic 52 (3-4):295-316 (2013)
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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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10.1007/s00153-012-0317-4

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Citations of this work

Monadic NM-algebras.Juntao Wang, Pengfei He & Yanhong She - 2019 - Logic Journal of the IGPL 27 (6):812-835.

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References found in this work

Zum intuitionistischen aussagenkalkül.K. Gödel - 1932 - Anzeiger der Akademie der Wissenschaften in Wien 69:65--66.
First-order Gödel logics.Richard Zach, Matthias Baaz & Norbert Preining - 2007 - Annals of Pure and Applied Logic 147 (1):23-47.
On the structure of rotation-invariant semigroups.Sándor Jenei - 2003 - Archive for Mathematical Logic 42 (5):489-514.

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