Completeness Of SLDNF-Resolution For Non-Floundering Queries

Abstract

this paper we show that SLDNF-resolution is complete for non-floundering goals under some natural conditions concerning fairness. The novelty of our approach is that we relate the completeness directly to non-floundering and we deal with arbitrary normal programs and goals. The paper is organized as follows. The next section contains the outline of the paper. Section 3 presents the concepts necessary for our work. Among others we need a constraint representation of resolution where instead of applying mgu's the corresponding equations are added to the goals. That section also presents SLDFA-resolution [Dra95] which is a generalization of SLDNF-resolution for constructive negation. A completeness result for SLDFA-resolution [Dra95] is a starting point for our work. The next two sections introduce SLDNF1-resolution and discuss floundering. SLDNF1-resolution can be seen as an alternative definition of SLDNF-resolution. We introduce it in order to be able to deal with fairness. Section 6 presents our completeness results for SLDNF1-resolution and for SLDNFresolution. The last section shows how 3-valued completion semantics can be represented in a standard 2-valued logic. We assume that the reader is familiar with basics of logic programming, SLDNFresolution [Llo87] and the Kunen semantics [Kun87].