Loop Formulas for Alog Answer Set Programs

Abstract

Logic programming based on answer set semantics, coined Answer Set Programming, is an important declarative problem solving paradigm. It has been widely used in various fields, such as artificial intelligence, bioinformatics, linguistics and so forth. Lin and Zhao's notion of loop formulas for normal logic programs provides not only a deep understanding for answer set semantics but also an alternative approach of computing answer sets in terms of satisfiability solvers. Gelfond and Zhang recently propose a new semantics -- Alog answer sets -- for logic programs with aggregates, that is a distinguishing extension for normal logic programs. This paper generalizes Lin and Zhao's loop formulas to these logic programs and shows that, together with completion, loop formulas can capture the new semantics. Thus, it provides an alternative understanding for this semantics and a potential approach of computing Alog answer sets.