Development of Relational Event Algebra Proper to Address Data Fusion Problems

Abstract

For completeness, relational events representing weighted linear combinations of multiple event probabilities or polynomial or analytic functions of one probability variable, in Sections 16.1 and 16.2, which have been already treated in [2], [3], are again presented here. New corrected results concerning relational events representing quadratic polynomials in two event probability variables are given in Section 16.3. Finally, Section 16.4 provides new results on representing various functions of event probabilities, which up to now, were thought to be unrepresentable, including minimum and maximum, multiplication by integers exceeding unity, bounded sums, and absolute differences — and dp,1. The device used to carry this out is to relax the requirement that the relational event in question be independent of any particular choice of probability evaluation. In particular, the constant-probability events (but, not the ordinary or other conditional events involved) of the relational events are allowed to be dependent on the probability measure chosen for evaluation. Finally, a number of open questions concerning conditional and relational event algebra are presented in Section 16.5.