Mutually Exclusive Nuances of Truth in Moisil Logic

Published in Volume XXV, Issue 1, 2015, pages 69-88, doi: 10.7561/SACS.2015.1.69

Authors: D. Diaconescu, I. Leuștean

Abstract

Moisil logic, having as algebraic counterpart Łukasiewicz-Moisil algebras, provides an alternative way to reason about vague information based on the following principle: a many-valued event is characterized by a family of Boolean events. However, using the original definition of Łukasiewicz-Moisil algebra, the principle does not apply for subalgebras. In this paper we identify an alternative and equivalent definition for the n-valued Łukasiewicz-Moisil algebras, in which the determination principle is also saved for arbitrary subalgebras, which are characterized by a Boolean algebra and a family of Boolean ideals. As a consequence, we prove a duality result for the n-valued Łukasiewicz-Moisil algebras, starting from the dual space of their Boolean center. This leads us to a duality for MVn-algebras, since are equivalent to a subclass of n-valued Łukasiewicz-Moisil algebras.

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Bibtex

@article{sacscuza:diaconescu2015menotiml,
  title={Mutually Exclusive Nuances of Truth in Moisil Logic},
  author={D. Diaconescu and I. Leu{c s}tean},
  journal={Scientific Annals of Computer Science},
  volume={25},
  number={1},
  organization={``A.I. Cuza'' University, Iasi, Romania},
  year={2015},
  pages={69--88},
  doi={10.7561/SACS.2015.1.69},
  publisher={``A.I. Cuza'' University Press}
}