A Well-Founded Semantics for FOL-Programs

ABSTRACT. An FOL-(logic) program consists of a background theory in a decidable fragment of first-order logic and a collection of rules possibly containing first-order formulas. The formalism stems from recent approaches to tight integrations of ASP with description logics. In this paper, we investigate whether and how we can define well-founded and stable semantics of FOL-programs uniformly under the approximation fixpoint theory. We develop an extended theory that treats consistent as well as inconsistent pairs on a bilattice. We then apply the extended theory to FOL-programs to define the well-founded and stable semantics for FOL-programs, and show some relationships with the semantics defined using different methods. The work reported here shows how consistent approximations may be extended to capture wider classes of logic programs whose semantics can be treated uniformly.