Normal Forms of Conditional Knowledge Bases Respecting Entailments and Renamings

Abstract

Normal forms of conditional knowledge bases are useful to create, process and compare the knowledge represented by them. In this paper, we propose the reduced antecedent normal form (RANF) for conditional knowledge bases. Compared to the antecedent normal form, it represents conditional knowledge with significantly fewer conditionals. A set of transformation rules maps every knowledge base to a model equivalent knowledge base in RANF. The new notion of renaming normal form (\(\rho \)NF) of a conditional knowledge base takes signature renamings into account. We develop an algorithm for systematically generating conditional knowledge bases over a given signature that are both in RANF and in \(\rho \)NF. The generated knowledge bases are consistent, pairwise not antecedentwise equivalent and pairwise not equivalent under signature renaming. Furthermore, the algorithm is complete in the sense that, taking signature renamings and model equivalence into account, every consistent knowledge base is generated.