$\mathcal{R}\mathcal{E}\mathcal{S}$: A formalism for reasoning with relative-strength defaults

Abstract

$\mathcal{R}\mathcal{E}\mathcal{S}$ is a system for reasoning about evidential support relationships between statements[1, 2]. In $\mathcal{R}\mathcal{E}\mathcal{S}$, the preferences of these supports are represented symbolically, by directly comparing them, instead of by numerical degrees. Z⁺ is a formalism for reasoning with variable-strength defaults[5] which provides a mechanism to compute a minimum admissible ranking for models (subject to the consistency condition) from the given integer strengths of defaults.

In this paper, we combine the two systems. We show that the same consistency condition of Z ⁺ can be applied to $\mathcal{R}\mathcal{E}\mathcal{S}$ even though the preferences of rules are represented as a relation in $\mathcal{R}\mathcal{E}\mathcal{S}$. A similar procedure is devised which can produce the admissible relative strengths (a relation) and can produce the relation on models with respect to the strengths of the rules they violate. A consequence relation is defined and a procedure to answer queries concerning it is devised. The resulting system, also called $\mathcal{R}\mathcal{E}\mathcal{S}$, is then compared to Z ⁺. We show that, while $\mathcal{R}\mathcal{E}\mathcal{S}$ is very similar to Z ⁺ and displays comparable reasoning processes most of the time, they are not the same and $\mathcal{R}\mathcal{E}\mathcal{S}$ is more in agreement with common sense in some situations. Comparing $\mathcal{R}\mathcal{E}\mathcal{S}$ to the stratified ranking system [6] shows that $\mathcal{R}\mathcal{E}\mathcal{S}$, as presented, also shares some limitations with Z ⁺