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Preferential Entailments, Extensions and Reductions of The Vocabulary

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». Firstly, we show how an extension of the vocabulary allows to express any preferential entailment as a preferent- ial entailment without state. Secondly, by reducing the vocabulary, we show how to express some preferential entailments in a smaller language. This second method works only for particular preferential entailments, including the widely used circumscription. For our purpose, we need to make precise the operations of extension or reduction of the vocabulary, which may have applications in other domains. We study which properties of an inference operation are preserved by the reduction and extension of the vocabulary introduced in this text. We provide examples of applications of our results. These applications are all related to various kinds of circumscriptions, because this suffices to provide examples of useful and non trivial results. Moreover, our study shows that many preferential entailments of the two kinds may be easily expressed in terms of circumscripti- on. All along the text, we take great care in providing constructive definitions, and to keep these constructions as simple and natural as possible.
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Submitted on : Wednesday, May 24, 2006 - 11:08:54 AM
Last modification on : Friday, May 20, 2022 - 9:04:45 AM
Long-term archiving on: : Sunday, April 4, 2010 - 11:25:55 PM

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  • HAL Id : inria-00072872, version 1

Citation

Yves Moinard, Raymond Rolland. Preferential Entailments, Extensions and Reductions of The Vocabulary. [Research Report] RR-3787, INRIA. 1999. ⟨inria-00072872⟩

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