Abstract: Imprecise Probabilities and Their Role.., By Dr. Matthew Ikle'
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Abstract posted for the May 20-21 AGI Workshop: Imprecise Probabilities and Their Role in General Intelligence By: Dr. Matthew Ikle', Adams State College, Department of Mathematics and Computer Science; and Novamente LLC The ability to reason upon incomplete and uncertain information is clearly an important attribute of any generally intelligent system. What is, perhaps, not as obvious is the role of imprecision in this reasoning ability. However, it is being increasingly acknowledged in the research community that the capability of effectively managing uncertainty in the context of complex inferences on large amounts of information is a critical aspect of intelligence. One popular approach to uncertain reasoning is classical Bayesian inference, which is founded upon the premise that all information, and hence uncertainty, obeys a single underlying precise probability distribution. Imprecise probability, on the other hand, is a generic term often used to represent any of a variety of less sharp, through no less rigorous, measurements of uncertainty. In his seminal work, Statistical Reasoning With Imprecise Probabilities, Peter Walley argues that it is more natural and consistent to represent probabilities as intervals than as a single precise value. Kurt Weichelsberger provides an alternate axiomatic approach to imprecise probabilities that provides similar interval-valued probabilities. One practical issue with using interval probabilities in the context of probabilistic inference rules, however, is the pessimism implicit in interval arithmetic. If one takes traditional probabilistic calculations and replaces the probabilities with intervals, then one finds that the intervals rapidly expand to the interval [0,1]. Walley's, Weichelsberger's and other contemporary approaches to imprecise probabilities suffer from this problem in various forms in spite of their mathematical and statistical sophistication. To overcome this deficiency, we have developed a new approach to handling incomplete and uncertain knowledge. Using probability distribution envelopes, we generalize both Walley's model and the standard Bayesian model. As a result, standard Bayesian inference models and imprecise probability models both reduce to special cases of a more general principle. In the context of artificial general intelligence, our new envelope-based approach provides AI architects with unprecedented flexibility. In the context of our Probabilistic Logic Network (PLN) reasoning system (developed for use within the Novamente AI Engine), we demonstrate how our generalized notion of imprecise probabilities allow for heuristic rules, classical Bayesian inference rules, and imprecise probability rules to interoperate with ease.  PPT: Imprecise Probabilities and Their Role in General IntelligenceImportant Links: Main Workshop Website: http://www.agiri.org/workshop Directions/Hotel: http://www.agiri.org/directions.htm Workshop Schedule: http://www.agiri.org/schedule.htm Printable Version / Handout: http://www.agiri.org/workshop/AGIRI_Workshop_2006.pdf 
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