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. As well, we 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, for which we provide characterizations in terms of graph conditions. 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.

From Logic Programs Updates to Action Description Updates

“…⊕ P n a set of stable models (that is proven there to coincide with the stable models semantics when the sequence is formed by a single normal [11] or generalized program [22]). The rationale for the definition of a stable model M of a DLP is made in accordance with the causal rejection principle [10,19]: If the body of a rule in a given update is true in M , then that rule rejects all rules in previous updates that are conflicting with it. Such rejected rules are ignored in the computation of the stable model.…”

“…In recent years some effort was devoted to explore and study the problem of how to update logic programs with new rules [3,8,10,19,20,17]. Here, knowledge is conveyed by sequences of programs, where each program in a sequence is an update to the previous ones.…”

Updates in answer set programming: An approach based on basic structural properties

“…Causal rejection enforces that in case of conflicts between rules, more recent rules are preferred and older rules are overridden (Eiter et al 2002). As was noted in (Eiter et al 2002), causal rejection is not novel, and what they provided was a simple and rigorous realization of this principle, as well as the formalization of a semantics for updating logic programs based on it. We developed the present work based on this principle also, aiming to express program updates succinctly while preserving relevant properties.…”

“…In our work we analyze the approach presented in (Eiter et al 2002) because under this approach a program is explicitly constructed. We believe that this is important from a computational perspective and also that such an approach is more suitable to study the properties of updates based on the causal rejection principle, since it provides insight into the operation of the principle itself.…”

“…We believe that this is important from a computational perspective and also that such an approach is more suitable to study the properties of updates based on the causal rejection principle, since it provides insight into the operation of the principle itself. We go a step further by presenting an alternative but equivalent definition of update sequences as presented in (Eiter et al 2002), for the case when considering two programs and that avoids the need of new atoms. We consider our definition to be more concise and accessible.…”