Algebraic-geometric structures for uncertainty

A simple observation is presented, although the mathematical methods used are not elementary, about the fact that some key concepts in uncertainty such as dependent/independent events or conditional events, can be represented using the local concept of truth. Intuitively the shift from global to local truth can be represented as the shift from the question of "whether" the proposition p is true to the question of "where" the proposition p is true. A method is defined to give a formal definition of local truth for an uncertainty-based universe of sets. To this aim, a universe of generalized sets is defined as the topos of presheaves on a suitable topological space, that formalizes the idea of where. As it is known, sets in such a universe are variable objects, governed by a local idea of truth. Some aspects of uncertainty are described in this formalism