Toward a More Comprehensive Theory of Conditional Events and Conditional Event Algebra.

摘要

Conditional events are the algebraic counterpart for all probability evaluations leading to corresponding conditional probabilities. analogous to the role that is enjoyed by boolean algebra relative to all unconditional probability evaluations. This paper is in two parts. First, a review of the basic problem is presented, encompassing motivations, basic issues, and the Lewis triviality result, Second, a new approach to conditional event algebra is presented. This approach utilizes a product space construction and leads to a boolean setting for the conditional events. In turn, this yields a system, which unlike all previous attempts, produces a fully satisfactory answer to a number of issues, including the nested or higher order conditioning problem and the problem of compatibility with independent information, among others. (AN).