A Review on Theory of Conditional Event Algebra
Yong Sheng Deng · Chinese Journal of Computers · 2003
Multiple source information forms one of the key components of data fusion. Such information may emanate from various mechanical sensor sources such as radar or Doppler systems, or it may derive from human-based sources, such as via expert opinion expressed through natural language. In general, each unit information is associated with degree of uncertainty/certainty which is traditionally determined through the use of probability. Thus, one can evaluate probabilistically any desired logical combination of events for use in decision-making. On the other hand, information uncertainty is provided in a way that there appears to be no single underlying Boolean event whose probability evaluation matches the prescribed uncertainty. Such uncertainty is often expressed in the form of given functions of probability evaluations of contributing simpler events. For example, when these functions are simple arithmetic divisions with arguments being pairs of events, each numerator argument event being a subevent of the denominator argument event, the quantitative uncertainty corresponding to each unit of information then, becomes a conditional probability. But, in general, the standard development of probability theory and statistics has not produced a way to represent conditional probabilities as single event probability evaluations, so that standard statistical decision-making techniques cannot be used in systematic sound way here. Recently, probability theory has been expanded to address the problem in the form of conditional event algebra. Conditional Event Algebra (CEA) is a relatively new logic system which rigorously extends standard probability theory to include events which are contingent such as rules and conditionals. if ...then is modeled as Boolean elements, and yet compatible with conditional probability quantitative value. The principle theory and application of conditional event algebra is presented. We also introduce the idea of relational event algebra which is more general than conditional event algebra.