Stable versus Layered Logic Program Semantics

For practical applications, the use of top-down query-driven proofprocedures is convenient for an efficient use and computation of answers using Logic Programs as knowledge bases. Additionally, abductive reasoning on demand is intrinsically a top-down search method. A 2-valued semantics for Normal Logic Programs (NLPs) allowing for top-down query-solving is thus highly desirable, but the Stable Models semantics (SM) does not allow it, for lack of the relevance property. To overcome this limitation we introduced in [24], and review here, a new 2-valued semantics for NLPs — the Layer Supported Models semantics — which conservatively extends the SM semantics, enjoys relevance and cumulativity, guarantees model existence, and respects the Well-Founded Model. In this paper we also exhibit a transformation, TR, from one propositional NLP into another, whose Layer Supported Models are precisely the Stable Models of the transform, which can then be computed by extant Stable Model implementations, providing a tool for the immediate generalized use of the new semantics and its applications. In the context of abduction in Logic Programs, when finding an abductive solution for a query, one may want to check too whether some other literals become true (or false) as a consequence, strictly within the abductive solution found, that is without performing additional abductions, and without having to produce a complete model to do so. That is, such consequence literals may consume, but not produce, the abduced literals of the solution. To accomplish this mechanism, we present the concept of Inspection Point in Abductive Logic Programs, and show, by means of examples, how one can employ it to investigate side-effects of interest (the inspection points) in order to help choose among abductive solutions.