First-order Nilpotent Minimum Logics: first steps
Abstract
Following the lines of the analysis done in [BPZ07, BCF07] for first-order G\"odel logics, we present an analogous investigation for 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. We establish 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
Cite
@article{arxiv.1103.6025,
title = {First-order Nilpotent Minimum Logics: first steps},
author = {Matteo Bianchi},
journal= {arXiv preprint arXiv:1103.6025},
year = {2012}
}
Comments
In this version of the paper the presentation has been improved. The introduction section has been rewritten, and many modifications have been done to improve the readability; moreover, numerous references have been added. Concerning the technical side, some proofs has been shortened or made more clear, but the mathematical content is substantially the same of the previous version