Computing Loops with at Most One External Support Rule for Basic Logic Programs with Arbitrary Constraint Atoms

The well-founded semantics of logic programs is not only an important semantics but also serves as an essential tool for program simplification in answer set computations. Recently, it has been shown that for normal and disjunctive programs, the well-founded models can be computed by unit propagation on program completion and loop formulas of loops with no external support. An attractive feature of this approach is that when loop formulas of loops with exactly one external support are added, consequences beyond the well-founded model can be computed, which sometimes can significantly speed up answer set computation. In this paper, we extend this approach to basic logic programs with abstract constraint atoms. We define program completion and loop formulas and show how to capture the well-founded semantics that approximate answer sets of basic logic programs. We show that by adding the loop formulas of loops with one external support, consequences beyond well-founded models can be computed. Our experiments show that for certain logic programs with constraints accepted by lparse, the consequences computed by our algorithms can speed up current ASP solvers smodels and clasp.