Plausibility Measures and Default Reasoning

TL;DR

This paper introduces plausibility measures as a unified framework for modeling uncertainty and applies it to default reasoning, showing that various existing semantics are almost always compatible with the KLM axioms within this framework.

Contribution

It provides a unifying approach to uncertainty modeling and characterizes the conditions under which the KLM axioms are sound and complete for default reasoning.

Findings

Plausibility measures generalize probability, belief, and possibility measures.

The KLM axioms are nearly always sound and complete within the plausibility framework.

Existing default reasoning semantics satisfy the necessary conditions for the KLM axioms.

Abstract

We introduce a new approach to modeling uncertainty based on plausibility measures. This approach is easily seen to generalize other approaches to modeling uncertainty, such as probability measures, belief functions, and possibility measures. We focus on one application of plausibility measures in this paper: default reasoning. In recent years, a number of different semantics for defaults have been proposed, such as preferential structures, $\epsilon$-semantics, possibilistic structures, and $\kappa$-rankings, that have been shown to be characterized by the same set of axioms, known as the KLM properties. While this was viewed as a surprise, we show here that it is almost inevitable. In the framework of plausibility measures, we can give a necessary condition for the KLM axioms to be sound, and an additional condition necessary and sufficient to ensure that the KLM axioms are complete. This additional condition is so weak that it is almost always met whenever the axioms are sound. In particular, it is easily seen to hold for all the proposals made in the literature.