New Results on the Compatibility of the Standard Conditional Likelihood Approachwith Product Space Conditional Event Algebra. (Reannouncement with New Availability Information)

摘要

It is an understatement that information in general arrives in conditional form.In fact, unconditional information can always be considered as the special case where the antecedent is universal. Nevertheless, it is surprising how little progress has been made in developing a full logic of conditional expressions, compatible with traditional conditional probability techniques. Recently, this problem has begun to be addressed by a number of researchers, who have commonly agreed that, as a basis, conditional events (a/b), where a and b are ordinary unconditional ones lying in some sample space (boolean or sigma-algebra), should be interpreted as intervals of events (or their logical equivalence) A*B, B' V A*B, relative to the usual event or set partial order less than or equal. Following this a number of conditional event algebras have been derived/proposed, possessing several desirable mathematical-logical properties and relatively easy to implement. (See, e.g. Goodman, Nguyen, and Walker, Conditional Inference and Logic for Intelligent Systems. A Theory of Measure-Free Conditioning, North-Holland, 1991.) However, a major drawback with these algebras is that inherently they cannot be boolean. (At most, they can have an algebraic structure which is a Stone algebra-see the above reference.) This leads, in particular, to certain problems in relating this work to the standard numerically-oriented approach of conditional probability, including the modeling of random variables and higher order conditional forms.... Data fusion, Semantics, Conditional events, Linguistic information, Syntactics.