On the proper definition of minimality in specialization and theory revision

Abstract

A central operation in an incremental learning system is the specialization of an incorrect theory in order exclude incorrect inferences. In this paper, we discuss what properties are to be required from such theory revision operations. In particular, we examine what it should mean for a revision to be minimal. As a surprising result, the seemingly most natural criterion, requiring revisions to produce maximally general correct specializations, leads to a number of serious problems. We therefore propose an alternative interpretation of minimality based on the notion of base revision from theory contraction work, and formally define it as a set of base revision postulates. We then present a revision operator (Mbr) that meets these postulates, and shown that it produces the maximally general correct revision satisfying the postulates, i.e., the revisions produced by Mbr are indeed minimal in our sense. The operator is implemented and used in Krt, the knowledge revision tool of the Mobal system.