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 and reveal their close connections to the notion of forgetting in classical propositional theories. Based on these notions, we then propose a framework for conflict solving in logic programs, which is general enough to represent many important conflict solving problems. We also study some essential semantic and computational properties in relation to strong and weak forgettings and conflict solving in our framework.