Real Functions in stochastic dependence

Abstract

In a fuzzied probability theory, random events are modeled by measurable functions into [0,1] and probability measures are re-
placed by probability integrals. The transition from Boolean two-valued logic to  Lukasiewicz multivalued logic results in an upgraded probability theory in which we define and study asymmetrical stochastic dependence/independence and conditional probability based on stochastic channels and joint experiments so that the classical constructions follow as particular cases. Elementary categorical methods enable us to put the two theories into a perspective.