Keynote Address Abstract

Classical Boolean events stand to continuous events as yes-no observables stand to observables with bounded continuous spectrum. We first show that Lukasiewicz logic has a universal role in the representation of (de Finetti coherent) probability assessments of continuous events. We then approach the problem of defining a conditional for continuous events, as a map (F, G) → P(F, G), read "the probability of F given G", from pairs of formulas to real numbers in. P is required to satisfy Renyi\´s axiom of compound probabilities, as well as the following substitutivity axiom: P(F, G) = P(X, G∧(X ↔ F)) whenever X is a variable not occurring in F and G. We show that Lukasiewicz logic allows a conditional having these, together with many other desirable properties.