Probabilities and reasoning about possibilities

AbstractThis paper explores the relationship between probabilistic and symbolic approaches to reasoning under uncertainty. The principal result is that symbolic and quantitative approaches interact in interesting, sometimes counterintuitive ways. There are several reasons for believing that over multiple domains and applications, propositions true in most (few) of the possible states enumerated by a symbolic reasoning system will usually (rarely) be true. This result does not necessarily depend on the “true” probability of the possible states. Regarding attempts to merge symbolic and probabilistic procedures, it is shown that this is a fundamentally difficult problem. An automated system that assigns probabilities after a possibility space has been specified will either promote inappropriate probability estimates or perform redundant processing. Alternatively, one could use an approach that combines probabilities with possibility ratios to generate belief values that are guaranteed to satisfy certain calibration properties, but this generally requires ignoring some “known” probabilities