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Non-standard theories of uncertainty in knowledge representation and reasoning(1)

Published online by Cambridge University Press:  07 July 2009

Didier Duboid  and
Henri Prade
Didier Duboid
Affiliation:
Institut de Recherche en Inforinatique de Toulouse (IRIT)—CNRS Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex, France
Henri Prade
Affiliation:
Institut de Recherche en Inforinatique de Toulouse (IRIT)—CNRS Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex, France
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Abstract

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.

Type
Research Article
Information
The Knowledge Engineering Review , Volume 9 , Issue 4 , December 1994 , pp. 399 - 416
Copyright
Copyright © Cambridge University Press 1994

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