Query answering under the any-world assumption for normal logic programs

Recently, Loyer and Straccia have defined the Any-World Assumption (AWA) for normal logic programs as a generalization of the well-known notions of Closed World Assumption (CWA) and the Open World Assumption (OWA). The AWA allows any assignment (i.e. interpretation), over a truth space (bilattice), to be a default assumption and, thus, the CWA and OWA are just special cases. While a declarative and a fixed-point characterization for normal logic programs under the AWA has been given, the topic of this paper is to provide a simple, yet general top-down query answering procedure for this setting.