An overview of possibilistic handling of default reasoning, with experimental studies

Salem Benferhat

Jean F. Bonnefon

Rui da Silva Neves

pp. 53-70

in: Gerhard Schurz, Hannes Leitgeb (eds), Non-monotonic and uncertain reasoning in cognition, Synthese 146, 2005.

Abstract

This paper first provides a brief survey of a possibilistic handling of default rules. A set of default rules of the form, “generally, from α deduce β”, is viewed as the family of possibility distributions satisfying constraints expressing that the situation where α and β is true has a greater plausibility than the one where a and - β is true. When considering only the subset of linear possibility distributions, the well-known System P of postulates proposed by Kraus, Lehmann and Magidor, has been obtained. We also present two rational extensions: one based on the minimum specificity principle and the other is based on the lexicographic ordering. The second part of the paper presents an empirical study of three desirable properties for a consequence relation that capture default reasoning: Rationality, Property Inheritance and Ambiguity Preservation. An experiment is conducted to investigate 13 patterns of inference for the test of these properties. Our experimental apparatus confirms previous results on the relevance of System P, and enforces the psychological relevance of the studied properties.