On Redundancy Elimination Tolerant Scheduling Rules

TL;DR

This paper introduces a new scheduling rule framework that is tolerant to redundancy elimination in logic programming, ensuring program termination and completeness are preserved.

Contribution

It proposes a novel priority-based atom scheduling model and characterizes a class of rules that maintain correctness despite redundancy elimination.

Findings

Redundancy elimination can affect termination and completeness.

A new class of scheduling rules called stack-queue rules is identified.

Stack-queue rules are shown to be tolerant to redundancy elimination.

Abstract

In (Ferrucci, Pacini and Sessa, 1995) an extended form of resolution, called Reduced SLD resolution (RSLD), is introduced. In essence, an RSLD derivation is an SLD derivation such that redundancy elimination from resolvents is performed after each rewriting step. It is intuitive that redundancy elimination may have positive effects on derivation process. However, undesiderable effects are also possible. In particular, as shown in this paper, program termination as well as completeness of loop checking mechanisms via a given selection rule may be lost. The study of such effects has led us to an analysis of selection rule basic concepts, so that we have found convenient to move the attention from rules of atom selection to rules of atom scheduling. A priority mechanism for atom scheduling is built, where a priority is assigned to each atom in a resolvent, and primary importance is given to the event of arrival of new atoms from the body of the applied clause at rewriting time. This new computational model proves able to address the study of redundancy elimination effects, giving at the same time interesting insights into general properties of selection rules. As a matter of fact, a class of scheduling rules, namely the specialisation independent ones, is defined in the paper by using not trivial semantic arguments. As a quite surprising result, specialisation independent scheduling rules turn out to coincide with a class of rules which have an immediate structural characterisation (named stack-queue rules). Then we prove that such scheduling rules are tolerant to redundancy elimination, in the sense that neither program termination nor completeness of equality loop check is lost passing from SLD to RSLD.