Approaches to Constructing a Stratified Merged Knowledge Base

Many merging operators have been proposed to merge either flat or stratified knowledge bases. The result of merging by such an operator is a flat base (or a set of models of the merged base) irrespective of whether the original ones are flat or stratified. The drawback of obtaining a flat merged base is that information about more preferred knowledge (formulae) versus less preferred knowledge is not explicitly represented, and this information can be very useful when deciding which formulae should be retained when there is a conflict. Therefore, it can be more desirable to return a stratified knowledge base as a merged result. A straightforward approach is to deploy the preference relation over possible worlds obtained after merging to reconstruct such a base. However, our study shows that such an approach can produce a poor result, that is, preference relations over possible worlds obtained after merging are not suitable for reconstructing a merged stratified base. Inspired by the Condorcet method in voting systems, we propose an alternative method to stratify a set of possible worlds given a set of stratified bases and take the stratification of possible worlds as the result of merging. Based on this, we provide a family of syntax-based methods and a family of model-based methods to construct a stratified merged knowledge base. In the syntax based methods, the formulae contained in the merged knowledge base are from the original individual knowledge bases. In contrast, in the model based methods, some additional formulae may be introduced into the merged knowledge base and no information in the original knowledge bases is lost. Since the merged result is a stratified knowledge base, the commonly agreed knowledge together with a preference relation over this knowledge can be extracted from the original knowledge bases.