On properties of update sequences based on causal rejection

Abstract

In this paper, we consider an approach to update nonmonotonic knowledge bases represented as extended logic programs under the answer set semantics. In this approach, new information is incorporated into the current knowledge base subject to a causal rejection principle, which enforces that, in case of conflicts between rules, more recent rules are preferred and older rules are overridden. Such a rejection principle is also exploited in other approaches to update logic programs, notably in the method of dynamic logic programming, due to Alferes et al.

One of the central issues of this paper is a thorough analysis of various properties of the current approach, in order to get a better understanding of the inherent causal rejection principle. For this purpose, we review postulates and principles for update and revision operators which have been proposed in the area of theory change and nonmonotonic reasoning. Moreover, some new properties for approaches to updating logic programs are considered as well. Like related update approaches, the current semantics does not incorporate a notion of minimality of change, so we consider refinements of the semantics in this direction. We also investigate the relationship of our approach to others in more detail. In particular, we show that the current approach is semantically equivalent to inheritance programs, which have been independently defined by Buccafurri et al., and that it coincides with certain classes of dynamic logic programs. In view of this analysis, most of our results about properties of the causal rejection principle apply to each of these approaches as well. Finally, we also deal with computational issues. Besides a discussion on the computational complexity of our approach, we outline how the update semantics and its refinements can be directly implemented on top of existing logic programming systems. In the present case, we implemented the update approach using the logic programming system DLV.