## Institute for Logic, Language and Computation

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# Tuesday 15 May 2001, 11.00, Computing with LLI Seminar, Joseph Halpern

Tuesday 15 May 2001, 11.00, Computing with LLI Seminar, Joseph Halpern
Speaker: Joseph Halpern (Cornell)
Title: Plausibility Measures and Default Reasoning
Date/Time: May 15, 2001, 11:00
Location: Room P.017, Euclides Building, Plantage Muidergracht 24, Amsterdam;

Abstract:
We introduce a new formalism for reasoning about uncertainty that we call {\em plausibility}. Plausibility is a generalization of probability: the plausibility of a set is just an element of some arbitrary partial order (instead of being an element of [0,1], as in the case of probability). We believe that plausibility will provide a reasonable generalization of probability that will allow more qualitative reasoning. We focus on one application of plausibility measures: default reasoning.

Defaults are statements like Birds typically fly''. In recent years, a number of different semantics for defaults have been proposed---involving such things as preference rankings, extreme probabilities, and possibility measures---that have been shown to be characterized by the same set of axioms, known as the KLM properties (for Kraus, Lehmann, Magidor). The fact that such disparate approaches were all characterized by the same axioms was viewed as quite surprising. We show that the KLM properties are almost inevitable, given some minimal properties. In the framework of plausibility measures, we can give a necessary condition for the KLM axioms to be sound, and an additional condition necessary and sufficient to ensure that the KLM axioms are complete. This additional condition is so weak that it is almost always met whenever the axioms are sound. In particular, it is easily seen to hold for all the proposals made in the literature.

In the literature, the focus has been on propositional default reasoning. We briefly consider the first-order case as well. Here it turns out that there are significant differences between the various proposals. Again, using plausibility helps us understand what is going on.

The talk is completely self-contained. (In particular, no previous knowledge of default reasoning is presumed.) It represents joint work with Nir Friedman.

Please note that this newsitem has been archived, and may contain outdated information or links.