On the Antecedent Normal Form of Conditional Knowledge Bases

摘要

Desirable properties of a normal form for conditional knowledge are, for instance, simplicity, minimality, uniqueness, and the respecting of adequate equivalences. In this paper, we propose the notion of antecedentwise equivalence of knowledge bases. It identifies more knowledge bases as being equivalent and allows for a simpler and more compact normal form than previous proposals. We develop a set of transformation rules mapping every knowledge base into an equivalent knowledge base that is in antecedent normal form (ANF). Furthermore, we present an algorithm for systematically generating conditional knowledge bases in ANF over a given signature. The approach is complete in the sense that, taking renamings and equivalences into account, every consistent knowledge base is generated. Moreover, it is also minimal in the sense that no two knowledge bases are generated that are antecedentwise equivalent or that are isomorphic to antecedentwise equivalent knowledge bases.