Polynomial Approximation to Well-Founded Semantics for Logic Programs with Generalized Atoms: Case Studies

The well-founded semantics of normal logic programs has two main utilities, one being an efficiently computable semantics with a unique intended model, and the other serving as polynomial time constraint propagation for the computation of answer sets of the same program. When logic programs are generalized to support constraints of various kinds, the semantics is no longer tractable, which makes the second utility doubtful. This paper considers the possibility of tractable but incomplete methods, which in general may miss information in the computed result, but never generates wrong conclusions. For this goal, we first formulate a well-founded semantics for logic programs with generalized atoms, which generalizes logic programs with arbitrary aggregates/constraints/dl-atoms. As a case study, we show that the method of removing non-monotone dl-atoms for the well-founded semantics by Eiter et al. actually falls into this category. We also present a case study for logic programs with standard aggregates.