Coping with the Limitations of Rational Inference in the Framework of Possibility Theory
Salem Benferhat, Didier Dubois, Henri Prade
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 counterintuitive 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 counterintuitive 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.
Keywords: Possibility theory, independence, nonmonotonic reasoning.
Pages: 9097
PS Link:
PDF Link: /papers/96/p90benferhat.pdf
BibTex:
@INPROCEEDINGS{Benferhat96,
AUTHOR = "Salem Benferhat
and Didier Dubois and Henri Prade",
TITLE = "Coping with the Limitations of Rational Inference in the Framework of Possibility Theory",
BOOKTITLE = "Proceedings of the Twelfth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI96)",
PUBLISHER = "Morgan Kaufmann",
ADDRESS = "San Francisco, CA",
YEAR = "1996",
PAGES = "9097"
}

