Tense operators on pseudo-MV algebras

Abstract

In this paper the concept of tense operators on a pseudo-MV algebra is introduced. Since a pseudo-MV algebra can be regarded as an axiomatization of noncommutative infinite-valued Łukasiewicz logic, these tense operators are considered to quantify the dimension, i.e. one expresses “it is always going to be the case that” and the other expresses “it has always been the case that”. We investigate basic properties of tense operators on pseudo-MV algebras and characterize the homomorphism of tense pseudo-MV algebras. Finally, we define a stronger version of tense pseudo-MV algebras and discuss the properties of filters under tense operators.