Coping with the Limitations of Rational Inference in the Framework of Possibility Theory

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.Comment: Appears in Proceedings of the Twelfth Conference on Uncertainty in Artificial Intelligence (UAI1996

A Plausibility Semantics for Abstract Argumentation Frameworks

We propose and investigate a simple ranking-measure-based extension semantics for abstract argumentation frameworks based on their generic instantiation by default knowledge bases and the ranking construction semantics for default reasoning. In this context, we consider the path from structured to logical to shallow semantic instantiations. The resulting well-justified JZ-extension semantics diverges from more traditional approaches.Comment: Proceedings of the 15th International Workshop on Non-Monotonic Reasoning (NMR 2014). This is an improved and extended version of the author's ECSQARU 2013 pape

Modelling default and likelihood reasoning as probabilistic

A probabilistic analysis of plausible reasoning about defaults and about likelihood is presented. 'Likely' and 'by default' are in fact treated as duals in the same sense as 'possibility' and 'necessity'. To model these four forms probabilistically, a logic QDP and its quantitative counterpart DP are derived that allow qualitative and corresponding quantitative reasoning. Consistency and consequence results for subsets of the logics are given that require at most a quadratic number of satisfiability tests in the underlying propositional logic. The quantitative logic shows how to track the propagation error inherent in these reasoning forms. The methodology and sound framework of the system highlights their approximate nature, the dualities, and the need for complementary reasoning about relevance