A theory of conditional information for probabilistic inference in intelligent systems: III. Mathematical appendix

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This paper concludes the work begun in Part I in presenting a coherent theory of conditioning consistent with all conditional probability evaluations. Part I presented the interval of events approach to conditional events, whereas Part II developed the Cartesian product space approach. Although the former is computationally feasible to implement, it lacks certain theoretical properties: in particular, it is non-Boolean in nature. On the other hand, the latter approach, although conceptually more desirable than the former—it leads to a unique Boolean structure—is much more complicated from a computation-implementation viewpoint. This paper presents the more technically detailed results required in the presentations of Parts I and II.