Reasoning about Priorities in Default Logic

Gerhard Brewka

In this paper we argue that for realistic applications involving default reasoning it is necessary to reason about the priorities of defaults. Existing approaches require the knowledge engineer to explicitly state all relevant priorities which are then handled in an extralogical manner, or they are restricted to priorities based on specificity, neglecting other relevant criteria. We present an approach where priority information can be represented within the logical language. Our approach is based on PDL, a prioritized extension of Reiter’s Default Logic recently proposed by the same author. In PDL the generation of extensions is controlled by an ordering of the defaults. This property is used here in the following way: we first build Reiter extensions of a given default theory. These extensions contain explicit information about the priorities of defaults. We then eliminate every extension E that cannot be reconstructed as a PDL extension based on a default ordering that is compatible with the priority information in E. An example from legal reasoning illustrates the power of our approach.

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