NONSTANDARD THEORIES OF UNCERTAINTY IN KNOWLEDGE REPRESENTATION AND REASONING

This paper provides a survey of the state of the art in plausible reasoning, that is exception tolerant reasoning under incomplete information. Three requirements are necessary for a formalism in order to cope with this problem: (i) making a clear distinction between factual information and generic knowledge; (ii) having a correct representation of partial ignorance; (iii) providing a nonmonotonic inference mechanism. Classical logic fails on requirements (i) and (iii), whilst the Bayesian approach does not fulfil (ii) in an unbiased way. In this perspective, various uncertainty modelling frameworks are reviewed: MYCIN-like fully compositional calculi, belief functions, upper and lower probability systems, and possibility theory. Possibility theory enables classical logic to be extended to layered sets of formulae, where layers express certainty levels. Finally, it is explained how generic knowledge can be expressed by constraints on possibility measures, and how possibilistic inferences can encode nonmonotonic reasoning in agreement with the Lehmann et al. postulates.