Relating Optimal Repairs in Ontology Engineering with Contraction Operations in Belief Change

Abstract

The question of how a given knowledge base can be modified such that certain unwanted consequences are removed has been investigated in the area of ontology engineering under the name of repair and in the area of belief change under the name of contraction. Whereas in the former area the emphasis was more on designing and implementing concrete repair algorithms, the latter area concentrated on characterizing classes of contraction operations by certain postulates they satisfy. In the classical setting, repairs and contractions are subsets of the knowledge base that no longer have the unwanted consequence. This makes these approaches syntax-dependent and may result in removal of more consequences than necessary. To alleviate this problem, gentle repairs and pseudo-constractions have been introduced in the respective research areas, and their connections have been investigated in recent work. Optimal repairs preserve a maximal amount of consequences, but they may not always exist. We show that, if they exist, then they can be obtained by certain pseudo-contraction operations, and thus they comply with the postulates that these operations satisfy. Conversely, under certain conditions, pseudo-contractions are guaranteed to produce optimal repairs. Recently, contraction operations have also been defined for concepts rather than for whole knowledge bases. We show that there is again a close connection between such operations and optimal repairs of a restricted form of knowledge bases.