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Archive for Mathematical Logic

, Volume 52, Issue 3–4, pp 295–316 | Cite as

First-order Nilpotent minimum logics: first steps

  • Matteo Bianchi
Article

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.

Keywords

Many-valued logics Varieties of lattices Nilpotent Minimum logic Decidability 

Mathematics Subject Classification (2000)

03B50 03B25 03C07 03G10 03G25 06B20 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of Mathematics “Federigo Enriques”Università degli Studi di MilanoMilanoItaly

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