Boolean algebras with an automorphism group: a framework for Łukasiewicz logic
|Title:||Boolean algebras with an automorphism group: a framework for Łukasiewicz logic|
|Journal:||Journal of Multiple-Valued Logic and Soft Computing|
|Pages:||51 - 67|
We introduce a framework within which reasoning according to Lukasiewicz logic can be represented. We consider a separable Boolean algebra endowed with a (certain type of) group of automorphisms; the pair will be called a Boolean ambiguity algebra. is meant to model a system of crisp properties; is meant to express uncertainty about these properties.
We define fuzzy propositions as subsets of which are, most importantly, closed under the action of . 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.