First-order Nilpotent Minimum logics: first steps

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Matteo Bianchi
Title: First-order Nilpotent Minimum logics: first steps
Journal: Archive For Mathematical Logic
Volume 52
Number 3-4
Pages: 295-316
Year: 2013
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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.