Exceptional Subclasses in Qualitative Probability

TL;DR

This paper extends System Z+ to allow inheritance across exceptional subclasses by adding new constraints, improving its reasoning capabilities without affecting database consistency.

Contribution

It introduces an extension to System Z+ that addresses its inheritance limitations by deriving additional world constraints from defaults.

Findings

The extension preserves the original system's consistency.

It enables inheritance across exceptional subclasses.

Comparative analysis with other default reasoning systems.

Abstract

System Z+ [Goldszmidt and Pearl, 1991, Goldszmidt, 1992] is a formalism for reasoning with normality defaults of the form "typically if phi then + (with strength cf)" where 6 is a positive integer. The system has a critical shortcoming in that it does not sanction inheritance across exceptional subclasses. In this paper we propose an extension to System Z+ that rectifies this shortcoming by extracting additional conditions between worlds from the defaults database. We show that the additional constraints do not change the notion of the consistency of a database. We also make comparisons with competing default reasoning systems.