Forgetting under the Well-Founded Semantics

Recently, the notion of forgetting has drawn considerable attention in the area of Knowledge Representation and Reasoning. The underlying idea is to discard a part of the knowledge base without affecting the derivations on, e.g., atoms that are not to be forgotten. Several recent papers consider forgetting under answer set semantics, but sometimes the well-founded semantics with data complexity P (instead of coNP) is preferable in applications. In this paper, we develop a notion of forgetting for normal logic programs under the well-founded semantics. We show that a number of desirable properties are satisfied by our approach, in particular, it approximates forgetting for normal logic programs under answer set semantics as well as forgetting in classical logic. Three different algorithms are presented that maintain the favorable computational complexity of the well-founded semantics when compared to computing answer sets, and whose output is at most of the size of the original program, while partly keeping its syntactical structure.