Recent use of relational event algebra, including comparisons, estimation and deductions for probability-functional models

A model of information is called probability-functional, if a numerically valued function f exists with range in the unit interval and arguments consisting of a collection of probabilities of contributing events. The function f may be obtained either explicitly or implicitly and the reliability or evaluation of the model can be considered naturally as the evaluation of f. Many examples of probability-functional models exist including: linear regression models, expert pooled opinion, natural language descriptions, and inference rule systems, among others. Recently, a new mathematical tool-relational event algebra-has been developed to treat such models from a more algebraic-based viewpoint than previously considered, resulting in the representation of each such model by a single-possibly complex event whose probability evaluation (in an appropriately chosen probability space extending the initial one containing the contributing events) matches the evaluation of f. This allows for deeper interaction among the models, as opposed to more standard numerical approaches which do not take into account the full logical relation between the models, but rather only the numerical/probabilistic distances. The purpose of this short paper is: First, to present some motivations for the development of relational event algebra. Second, to show how relational event algebra, in turn, gives rise to natural approaches to the problems of testing hypotheses, combining information (via a Frechet type of loss function resulting in an algebraic average), and deduction.