This paper addresses the apparent mismatch between the normative and descriptive literatures in the cognitive science of conditional reasoning. Descriptive psychological theories still regard material implication as the normative theory of the conditional. However, over the last 20 years in the philosophy of language and logic the idea that material implication can account for everyday indicati...

The Borel-Kolmogorov Paradox is typically taken to highlight a tension between our intuition that certain conditional probabilities with respect to probability zero conditioning events are well defined and the mathematical definition of conditional probability by Bayes’ formula, which looses its meaning when the conditioning event has probability zero. We argue in this paper that the theory of ...

We establish equivalence of several regular conditional probability properties and Radon space. In addition, we introduce the universally measurable disintegration concept and prove an existence result.

The Bayesian network is a powerful knowledge representation formalism; it is also capable of improving its precision through experience. Spiegelhalter et al. [1989] proposed a procedure for sequential updating forward conditional probabilities (FCP) in Bayesian networks of diameter 1 with a single parent node. The procedure assumes certainty for each diagnosis which is not practical for many ap...