Mutually exclusive nuances of truth in Moisil logic
Denisa Diaconescu, Ioana Leustean

TL;DR
This paper refines the algebraic framework of Moisil logic by providing an alternative definition that preserves the principle of reasoning about vague information in subalgebras, and establishes a duality theory for these algebras.
Contribution
It introduces an equivalent definition of ulusiewicz-Moisil algebras that maintains the determination principle in subalgebras and develops a duality theory for these algebras.
Findings
New equivalent definition of ulusiewicz-Moisil algebras.
Duality result for ulusiewicz-Moisil algebras based on Boolean centers.
Extension of duality to MV-algebras.
Abstract
Moisil logic, having as algebraic counterpart \L ukasiewicz-Moisil algebras, provide 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 \L ukasiewicz-Moisil algebra, the principle does not apply for subalgebras. In this paper we identify an alternative and equivalent definition for the -valued \L ukasiewicz-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 -valued \L ukasiewicz-Moisil algebras, starting from the dual space of their Boolean center. This leads us to a duality for MV-algebras, since are equivalent to a subclass of -valued \L ukasiewicz-Moisil…
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Taxonomy
TopicsAdvanced Algebra and Logic · Rough Sets and Fuzzy Logic · Multi-Criteria Decision Making
