An approach to stochastic processes via non-classical logic

Abstract

Within the infinitary variety of σ-complete Riesz MV-algebras RMVσ, we introduce the algebraic analogue of a random variable as a homomorphism defined on the free algebra in RMVσ. After a preliminary study of the proposed notion, we use it to define stochastic processes in the framework of non-classical logic (Łukasiewicz logic, more precisely) and we define stochastic independence.