Algebraic approach to tense operators (Q2799965)

In this monograph, the authors, using algebraic tools, present an algebraic axiomatization of tense logic and tense operators. Formalization of quantifiers in various algebras used in propositional logic is included. Also, a description of tense operators, their axiomatization and a solution of the representation problem for classical logic axiomatized by means of Boolean algebras are presented. Tense and modal operators on bounded ordered sets, on De Morgan posets, on quantum structures, on effect algebras are introduced in this book. It is shown how the representation problem can be solved for spaces of numerical events by means of parallel words. Finally, the authors consider tense and modal operators on residuated structures which naturally serve as an algebraic axiomatization of fuzzy logics. They introduce the concept of a fuzzy relation and the construction and the representation problem are treated using this relation.