Forgetting is an important mechanism for logic-based agent systems. A recent interest has been in the desirable properties of forgetting in answer set programming  (ASP)and their impact on the design of forgetting operators. It is known that some subsets of these propertiesare incompatible, i.e., they cannot be satisfied at the same time. In this paper, we are interested in the question onthe largest set Δ of pairs (Π, V), where Π is  a logic program and V is a set of atoms, such that a forgetting operator exists that satisfies all the desirable properties for each  (Π, V) in Δ.  We answer this question positively by discovering the precise condition under which the knowledge forgetting, a well-established approach to forgetting in ASP, satisfies the property of strong persistence, which leads to a sufficient and necessary condition for a forgetting operator to satisfy all the desirable properties proposed in the literature. We explore computational complexities on checking the condition and present a syntactic characterization which can serve as the basis of computing knowledge forgetting in ASP.

In this paper, we propose a semantic forgetting for arbitrary logic programs(or propositional theories) under answer set semantics,called HT-forgetting. The HT-forgetting preserves strong equivalence in the sense that strongly equivalent logic programs will remain strongly equivalent after forgetting the same set of atoms. The result of an HT-forgetting is always expressible by a logic program, and in particular, the result of an HT-forgetting in a Horn program is expressible in a Horn program; and a representation theorem shows that HT-forgetting can be precisely characterized by Zhang-Zhou's four forgetting postulates under the logic of here-and-there. We also reveal underlying connections between HT-forgetting and classical forgetting, and provide complexity results for decision problems.