This paper introduces an abductive framework for updating knowledge bases represented by extended disjunctive programs. We first provide a simple transformation from abductive programs to update programs which are logic programs specifying changes on abductive hypotheses. Then, extended abduction, which was introduced by the same authors as a generalization of traditional abduction, is computed by the answer sets of update programs. Next, different types of updates, view updates and theory updates are characterized by abductive programs and computed by update programs. The task of consistency restoration is also realized as special cases of these updates. Each update problem is comparatively assessed from the computational complexity viewpoint. The result of this paper provides a uniform framework for different types of knowledge base updates, and each update is computed using existing procedures of logic programming.
In deductive databases, integrity maintenance is often coupled with view updating @cite_48 . Concerning studies which handle integrity maintenance in nonmonotonic logic programs, @cite_44 @cite_39 merge transactions of view updates and integrity maintenance in SLDNF-like top-down procedures. These procedures are sound and @cite_44 is also complete for computing view updates satisfying integrity constraints in locally stratified logic programs. Abductive procedures in @cite_47 @cite_21 @cite_4 also check integrity constraints in the process of computing candidate hypotheses. Compared with these studies, our approach in is based on the computation of answer sets and is applicable to non-stratified, disjunctive, and extended logic programs.
@cite_4 @cite_48 @cite_21 @cite_39 @cite_44 @cite_47
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Abstract We propose an extension of the SLDNF proof procedure for checking integrity constraints in deductive databases. To achieve the effect of the simplification methods investigated by Nicolas [1982], Lloyd, Sonenberg, and Topor [1986], and Decker [1986], we use clauses corresponding to the updates as top clauses for the search space. This builds in the assumption that the database satisfied its integrity constraints prior to the transaction, and that, therefore, any violation of the constraints in the updated database must involve at least one of the updates in the transaction. Different simplification methods can be simulated by different strategies for literal selection and search. The SLDNF proof procedure needs to be extended to use as top clause any arbitrary deductive rule, denial, or negated fact, to incorporate inference rules for reasoning about implicit deletions resulting from other deletions and additions, and to allow an extended resolution step for reasoning forward from negated facts. When updating a knowledge base, several problems may arise. One of the most important problems is that of integrity constraints satisfaction. The classic approach to this problem has been to develop methods for checking whether a given update violates an integrity constraint. An alternative approach consists of trying to repair integrity constraints violations by performing additional updates that maintain knowledge base consistency. Another major problem in knowledge base updating is that of view updating, which determines how an update request should be translated into an update of the underlying base facts. We propose a new method for updating knowledge bases while maintaining their consistency. Our method can be used for both integrity constraints maintenance and view updating. It can also be combined with any integrity checking method for view updating and integrity checking. The kind of updates handled by our method are: updates of base facts, view updates, updates of deductive rules, and updates of integrity constraints. Our method is based on events and transition rules, which explicitly define the insertions and deletions induced by a knowledge base update. Using these rules, an extension of the SLDNF procedure allows us to obtain all possible minimal ways of updating a knowledge base without violating any integrity constraint. We describe the theory and implementation of a general theorem-proving technique for checking integrity of deductive databases recently proposed by Sadri and Kowalski. The method uses an extension of the SLDNF proof procedure and achieves the effect of the simplification algorithms of Nicolas, Lloyd, , and Decker by reasoning forwards from the update and thus focusing on the relevant parts of the database and the relevant constraints. During the process of updating a database, two interrelated problems could arise. On one hand, when an update is applied to the database, integrity constraints could become violated, thus falsifying database consistency. In this case, the integrity constraint maintenance approach tries to obtain additional updates to be applied to re-establish database consistency. On the other hand, when an update request consist on updating some derived predicate, a view updating mechanism must be applied to translate the update request into correct updates on the underlying base facts. In this paper, we propose a general framework to compare and classify current methods in the field of view updating and integrity constraint maintenance. In this sense, we classify them considering how they tackle with both problems and, we also state the main drawbacks these methods have.