Solving logic program conflict through strong and weak forgettings

We consider how to forget a set of atoms in a logic program. Intuitively, when a set of atoms is forgotten from a logic program, all atoms in the set should be eliminated from this program in some way, and other atoms related to them in the program might also be affected. We define notions of strong and weak forgettings in logic programs to capture such intuition, reveal their close connections to the notion of forgetting in classical propositional theories, and provide a precise semantic characterization for them. Based on these notions, we then develop a general framework for conflict solving in logic programs. We investigate various semantic properties and features in relation to strong and weak forgettings and conflict solving in the proposed framework. We argue that many important conflict solving problems can be represented within this framework. In particular, we show that all major logic program update approaches can be transformed into our framework, under which each approach becomes a specific conflict solving case with certain constraints. We also study essential computational properties of strong and weak forgettings and conflict solving in the framework.