Beyond Counter-Examples to Nonmonotonic Formalisms: A Possibility-Theoretic Analysis

In nonmonotonic reasoning, Lehmann's preferential System P is known to provide reasonable but very cautious conclusions, while the inference machinery may still remain too cautious or on the contrary provide counter-intuitive conclusions when using the rational closure inference. These two types of inference can be represented using a possibility theory-based semantics. Remedies to the above problems are proposed in this framework. It is shown that counter-examples to inference by rational closure are not due to the technique of selecting a unique ordering of interpretations but to the choice of a wrong ordering, not in accordance with the actual knowledge. Namely when a counterintuitive plausible conclusion of a set of defaults, is in its rational closure, but not in its preferential closure (in the sense of System P), it is always possible to repair the set of defaults so as to produce the desired conclusions.