An approach to stochastic processes via non-classical logic

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