Boolean algebras with an automorphism group: a framework for Łukasiewicz logic

From Mathfuzzlog
Jump to: navigation, search
Authors:
Thomas Vetterlein
Title: Boolean algebras with an automorphism group: a framework for Łukasiewicz logic
Journal: Journal of Multiple-Valued Logic and Soft Computing
Volume 14
Number
Pages: 51 - 67
Year: 2008





Abstract

We introduce a framework within which reasoning according to Lukasiewicz logic can be represented. We consider a separable Boolean algebra $ \mathcal B $ endowed with a (certain type of) group $ G $ of automorphisms; the pair $ ({\mathcal B},G) $ will be called a Boolean ambiguity algebra. $ \mathcal B $ is meant to model a system of crisp properties; $ G $ is meant to express uncertainty about these properties.

We define fuzzy propositions as subsets of $ \mathcal B $ which are, most importantly, closed under the action of $ G $. By defining a conjunction and implication for pairs of fuzzy propositions in an appropriate manner, we are led to the algebraic structure characteristic for Lukasiewicz logic.