Answer Set Programs with One Incremental Variable

In the past decade, Answer Set Programming ASP has emerged as a popular paradigm for declarative problem solving, and a number of answer set solvers have been developed. However, most existing solvers require variables occurring in a logic program to be bounded by some finite domains, which limits their applications in one way or another. In this paper, we introduce answer set programs with one incremental variable to overcome this limitation. Based on existing ASP solving techniques, an approach to solve answer set programs with one incremental variable is proposed, and a prototype solver is then developed based on this approach. By conducting some experiments, our approach is shown to be comparable to iClingo's modular domain description approach in the incremental problem solving setting.