Some remarks on the notion of transitions

Abstract

In this paper some reflections on the concept of transition are presented: groupoids are introduced as models for the construction of a ``generalized logic'' whose basic statements involve pairs of propositions which can be conditioned. In this sense, we could distinguish between classical probability theory where propositions can be conditioned if they have a non-zero intersection, from cases where ``non-local'' conditioning are allowed. The algebraic and geometrical properties of groupoids can be exploited to construct models of such non-local description.