The Logic of CMV-Algebras
Antonio Di Nola, Brunella Gerla, Ciro Russo
TL;DR
This paper explores the properties of CMV-algebras and introduces an expanded one-variable fragment of Lukasiewicz propositional logic with algebraic semantics based on CMV-algebras.
Contribution
It presents a new logical fragment whose semantics are grounded in the algebraic structure of CMV-algebras, expanding the understanding of their logical applications.
Findings
Properties of CMV-algebras are characterized.
An expanded logical fragment is introduced.
Semantic correspondence with CMV-algebras is established.
Abstract
In this paper, once recalled some properties of CMV-algebras, we introduce an expansion of the one-variable fragment of Lukasiewicz propositional logic whose algebraic semantics is the variety of CMV-algebras.
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Taxonomy
TopicsAdvanced Algebra and Logic · Rough Sets and Fuzzy Logic · Logic, Reasoning, and Knowledge