Confidence Relations as a Basis for Uncertainty Modeling, Plausible Reasoning, and Belief Revision

The aim of this position paper is to outline a unified view of plausible reasoning under incomplete information and belief revision, based on an ordinal representation of uncertainty. The information possessed by an agent is supposed to be made of three items: sure observations, generic knowledge and inferred contingent beliefs. The main notion supporting this approach is the confidence relation, a partial ordering of events which encodes the generic knowledge of an agent. Plausible inference is achieved by conditioning. The paper advocates the similarity between plausible reasoning with confidence relations and probabilistic reasoning. The main difference is that the ordinal approach supports the notion of accepted beliefs forming a deductively closed set, while probability theory is not tailored for it. The framework of confidence relations sheds light on the connections between some approaches to non-monotonic reasoning methods, possibilistic logic and the theory of belief revision. In particular the distinction between revising contingent beliefs in the light of observations and revising the confidence relation is laid bare.