A compromised characterization to belief revision

Abstract

This paper proposes a method for handling logically conflicting inputs into knowledge bases. Basically, it concerns reconciling conflicting inputs with the underlying theory, via restricting their consequences. The main idea is to update the database with as many consistent consequences of the inputs as possible, in the case that the inputs themselves are not allowed to be kept in it. And in the case that a revision applies, the idea is to keep as many as possible of the consistent consequences of the retracted sentences as a compromise. Resolving conflicting updates in dynamic databases, for instance, are frequent and critically important problems of real applications. Such problems require the revision of theories and knowledge bases. It is not realistic to aim for a generic approach in those cases, since theory revision is fundamentally dependent on application-specific mechanisms, principles and heuristics. The approach we propose here, caters for the specific case where compromised solutions for revising knowledge bases apply, when conflicts involving updates occur. In comparison with approaches that require preference between conflitting inputs, or that avoid them by cancelling them out completely, our approach fits as an alternative which provides more informative results. Examples of inputs include database updates, actions, and beliefs. In more practical terms, consider the situation where K is a database and A an input. Assume that A is inconsistent with K. Current belief revision/update approaches will keep A and maintain consistency by selecting some element from K to form a revised database, usually denoted by K*A. There is a lot of research in this area, both theorectical, e.g.: the AGM theory of belief revision, and algorithmic research, e.g.: Reason Mantenance Systems. Our aim is to offer an alternative approach, restricted to some specific applications, which is flexible enough to keep more data in K in the case of conflicts. We view the above situation as a conflict between two inputs (K and A) into an empty database, and we tackle the problem of reconciling these inputs. Under our approach, the conflicting input A is kept in K only in the case that A does not directly contradict K's integrity constraints, in which case a revision also applies in order to restore consistency. However, in the case that A is not allowed to be kept in K, its eventual consistent consequences, w.r.t. the existing data of K, are added to the database under the compromised policy of our approach. This way, instead of preventing updates to be performed, when they introduce inconsistency to the system, our approach proposes to generate the consequences of the conflicting inputs, and to get rid of the inconsistency, via a minimal number of retractions of those consequences. We expect the resulting database to be consistent w.r.t. the integrity constraints, and to retain a maximal subset of the consistent non-supported consequences. This reconciliation of conflicting inputs follows some specified postulates for compromised revision. Justifications for the proposed approach are mainly based on its practical applications. In particular, design processes, where one builds up the goal state of a particular task, via performances of intermediary updates. Within this procedure, compromised results of updates can help to build up the goal state, when conflicts arise. This is so because, in general, our approach provides more information about the setting, in order to carry on the application development. We also find applications in AI, in particular in theory revision, where our approach can provide a compromised way for revising a theory base with conflicting information.