Yves Moinard
General preferential entailments as circumscriptions
, ECSQARU 2001 (Symbolic and Quantitative Approaches to Reasoning and Uncertainty) , Springer-Verlag, LNAI , Vol. 2143 , 532--543 , sep , 2001

Abstract A ``preferential entailment'' is defined by a binary relation, or ``preference relation'', either among interpretations (or models) or among ``states'' which are ``copies of interpretations''. Only the models, or the states, minimal for this relation, are considered, and this notion provides a natural formalization of aspects of common sense reasoning such as rules with exceptions. We study the best known modification of the vocabulary which has been introduced in order to help the automatic computation of all these ``preferential entailments''. Firstly, we show how an extension of the vocabulary allows the expression of any preferential entailment as a classical preferential entailment (without state). Then, we reexamine the role of this extension in the computation of the best known classical preferential entailment: circumscription. We provide various examples, all related to circumscriptions, which is till now the only preferential entailment for which efficient systems exist. This study shows precisely how many kinds of preferential entailments can be easily expressed in terms of circumscriptions. In order to get a better understanding of the method, we examine which fundamental properties of reasoning are preserved by this modification of the vocabulary, thus providing a powerful technical tool allowing to determine whether the method can be applied or not. For our purpose, we need to clarify the operations of extension or reduction of the vocabulary, which may have applications in other domains, as these modifications are very frequent, but have not been studied a lot in recent works. We provide constructive definitions, which are kept as simple and natural as possible.


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