A consistency-based framework for merging knowledge bases

We present a framework for expressing various merging operators for belief sets. This framework generalises our earlier work on consistency-based belief revision and contraction. Two primary merging operators are identified: in the first approach, belief sources are consistently combined so that the result of merging knowledge bases K1,…,KnK1,…,Kn is a maximal consistent (if possible) set of formulas comprising the joint knowledge of the knowledge bases. This approach then accords with one's intuitions as to what a “merge” operator should do. The second approach is more akin to a generalised belief revision operator. Knowledge bases K1,…,KnK1,…,Kn are “projected” onto another (in the simplest case the knowledge base where only tautologies are known). Properties of these operators are investigated, primarily by comparing their properties with postulates that have been identified previously in the literature. Notably, the approach is independent of syntax, in that merging knowledge bases K1,…,KnK1,…,Kn is independent of how each KiKi is expressed. As well, we investigate the role of entailment-based and consistency-based integrity constraints, the interrelationships between these approaches and belief revision, and the expression of further merging operators.