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Coping with the limitations of rational inference in the framework of possibility theory

Abstract : Possibility theory offers a framework where both Lehmann's "preferential inference" and the more productive (but less cautious) "rational closure inference" can be represented. However, there are situations where the second inference does not provide expected results either because it cannot produce them, or even provide counter-intuitive conclusions. This state of facts is not due to the principle of selecting a unique ordering of interpretations (which can be encoded by one possibility distribution), but rather to the absence of constraints expressing pieces of knowledge we have implicitly in mind. It is advocated in this paper that constraints induced by independence information can help finding the right ordering of interpretations. In particular, independence constraints can be systematically assumed with respect to formulas composed of literals which do not appear in the conditional knowledge base, or for default rules with respect to situations which are "normal" according to the other default rules in the base. The notion of independence which is used can be easily expressed in the qualitative setting of possibility theory. Moreover, when a counter-intuitive plausible conclusion of a set of defaults, is in its rational closure, but not in its preferential closure, it is always possible to repair the set of defaults so as to produce the desired conclusion.
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https://hal-univ-artois.archives-ouvertes.fr/hal-03299836
Contributor : Fabien Delorme <>
Submitted on : Monday, July 26, 2021 - 4:56:20 PM
Last modification on : Friday, September 10, 2021 - 4:42:04 PM

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  • HAL Id : hal-03299836, version 1
  • ARXIV : 1302.3559

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Salem Benferhat, Didier Dubois, Henri Prade. Coping with the limitations of rational inference in the framework of possibility theory. 12th Conference on Uncertainty in Artificial Intelligence (UAI 1996), Aug 1996, Portland, Oregon, United States. pp.90-97. ⟨hal-03299836⟩

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