Analysing and measuring inconsistency
Systems for merging knowledge
Merging systems take a tuple of knowledgebases as input and produce a consistent knowledgebase in the output that preserves as much as possible of the input knowledge. So knowledge merging looses information in order to provide an acceptable consistent view of the conflicting input knowledge.
Approaches to merging systems are either syntactic or semantic. In syntactic approaches, the maximally consistent subsets of the union of the input knowledgebases are considered as candidates for the output. In contrast, in the semantic approaches, the models of the input knowledgebases and the models of candidate output knowledgebases are considered so that an acceptable compromise amongst the input knowledgebases is found. For example, the potential output knowledgebase that has models that are nearest to the models of the majority of the input knowledgebases is selected. Semantic approaches have a number of desirable properties that the syntactic approaches lack. However, the semantic approaches are restricted to propositional logic. Recently, a generalization of the semantic approaches has been proposed which is based on a notion of dilation, a way of weakening classes of models, and thereby allows merging of knowledgebases of first-order predicate logic. In addition, this generalization maintains many of theoretical advantages of the semantic approaches.