SLT-Resolution for the Well-Founded Semantics

TL;DR

This paper introduces SLT-resolution, a linear tabling method for efficiently evaluating the well-founded semantics of logic programs, combining the advantages of linearity and completeness.

Contribution

SLT-resolution extends SLDNF-resolution with tabling to achieve linear, sound, and complete evaluation of well-founded semantics, suitable for implementation in Prolog systems.

Findings

Resolves infinite loops and redundancy while maintaining linearity.

Achieves termination and soundness for programs with bounded-term-size.

Comparable time complexity to SLG-resolution, polynomial for function-free programs.

Abstract

Global SLS-resolution and SLG-resolution are two representative mechanisms for top-down evaluation of the well-founded semantics of general logic programs. Global SLS-resolution is linear for query evaluation but suffers from infinite loops and redundant computations. In contrast, SLG-resolution resolves infinite loops and redundant computations by means of tabling, but it is not linear. The principal disadvantage of a non-linear approach is that it cannot be implemented using a simple, efficient stack-based memory structure nor can it be easily extended to handle some strictly sequential operators such as cuts in Prolog. In this paper, we present a linear tabling method, called SLT-resolution, for top-down evaluation of the well-founded semantics. SLT-resolution is a substantial extension of SLDNF-resolution with tabling. Its main features include: (1) It resolves infinite loops and redundant computations while preserving the linearity. (2) It is terminating, and sound and complete w.r.t. the well-founded semantics for programs with the bounded-term-size property with non-floundering queries. Its time complexity is comparable with SLG-resolution and polynomial for function-free logic programs. (3) Because of its linearity for query evaluation, SLT-resolution bridges the gap between the well-founded semantics and standard Prolog implementation techniques. It can be implemented by an extension to any existing Prolog abstract machines such as WAM or ATOAM.