Systematic Generation of Conditional Knowledge Bases up to Renaming and Equivalence

Abstract

A conditional of the form “If A then usually B” establishes a plausible connection between A and B, while still allowing for exceptions. A conditional knowledge base consists of a finite set of conditionals, inducing various nonmonotonic inference relations. Sets of knowledge bases are of interest for, e.g., experimenting with systems implementing conditional reasoning and for empirically evaluating them. In this paper, we present an approach for systematically generating knowledge bases over a given signature. The approach is minimal in the sense that no two knowledge bases are generated that can be transformed into each other by a syntactic renaming or that are elementwise equivalent. Furthermore, the approach is complete in the sense that, taking renamings and equivalences into account, every consistent knowledge base is generated.