Completeness of SLDNF-Resolution for Non-Floundering Queries

W LODZIMIERZ DRABENT. SLDNF-resolution is a standard operational semantics for negation as ((nite) failure. For some programs and goals SLDNF-resolution is incomplete with respect to the Kunen semantics (program completion in 3-valued logic). Intuitively, the reason of incompleteness is oundering. This fact has however 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 non-oundering queries. For this we need an appropriate notion of oundering. 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 deenition of SLDNF-resolution. We also show how the 3-valued completion semantics can be expressed in terms of the classical 2-valued logic.