Completeness of SLDNF-resolution for nonfloundering queries

Abstract

SLDNF-resolution is a standard operational semantics for negation as (finite) failure. For some programs and goals, SLDNF-resolution is incomplete with respect to the Kunen semantics (program completion in three-valued logic). Intuitively, the reason for incompleteness is floundering. This fact, however, has not been proven formally. The existing papers study syntactic classes of programs and goals for which SLDNF-resolution is complete. We prove completeness of SLDNF-resolution for arbitrary programs, fair selection rules, and nonfloundering queries. For this, we need an appropriate notion of floundering. We introduce two versions of this notion, one simple but crude, the other more sophisticated. To be able to deal with fairness, we introduce an alternative definition of SLDNF-resolution. We also show how the three-valued completion semantics can be expressed in terms of the classical two-valued logic.