Nested Epistemic Logic Programs Kewen Wang 1 and Yan Zhang 2 1 Griffith University, Australia k.wang@griffith.edu.au 2 University of Western Sydney yan@cit.uws.edu.au Abstract. Nested logic programs and epistemic logic programs are two impor- tant extensions of answer set programming. However, the relationship between these two formalisms is rarely explored. In this paper we first introduce the epis- temic HT-logic, and then propose a more general extension of logic programs called nested epistemic logic programs. The semantics of this extension - named equilibrium views - is defined on the basis of the epistemic HT-logic. We prove that equilibrium view semantics extends both the answer sets of nested logic pro- grams and the world views of epistemic logic programs. Therefore, our work establishes a unifying framework for both nested logic programs and epistemic logic programs. Furthermore, we also provide a characterization of the strong equivalence of two nested epistemic logic programs. 1 Introduction Answer set programming (ASP) [6] was developed in the late of 1990s and has been widely recognized as a promising tool for effective knowledge representation and declar- ative problem solving [1]. ASP is based on the answer set semantics of logic programs introduced by Gelfond and Lifschitz [4, 5]. The formal systems for ASP may have dif- ferent features such as default negation, explicit negation, disjunction and preference. Normal, general, extended and disjunctive logic programs are among the major ASP formalisms. As many researchers (including [3, 8]) have noticed, the languages of logic pro- gramming are still insufficient in representing commonsense knowledge. Recently an- swer set semantics has been extended to nested logic programs [8], in which arbitrarily nested formulas are allowed. On the other hand, ASP is also expanded to epistemic logic programs by Gelfond [3], where belief operators can be explicitly presented so that incomplete information may be correctly represented in the extent of multiple be- lief sets. The semantics of epistemic logic programs is defined as the collection of its world views, which are generalizations of the answer sets for logic programs without nested expressions. Having examined the syntax and semantics of nested logic programs and epistemic logic programs, people may observe an important fact: Although the world view seman- tics of epistemic logic programs generalizes the answer set semantics for disjunctive (extended) logic programs, it, however, cannot be used as the semantics for the epis- temic logic programs with nested expressions containing belief operators. Hence, the following two problems remain open: