Linear Tabulated Resolution Based on Prolog Control Strategy

TL;DR

This paper introduces TP-resolution, a linear tabulated resolution method that combines loop checking and tabling to efficiently resolve infinite loops and redundant computations in Prolog, while maintaining simplicity and handling cuts effectively.

Contribution

It presents a novel linear tabulated resolution approach, TP-resolution, that is sound, complete, and compatible with existing Prolog abstract machines, improving upon non-linear methods.

Findings

Handles infinite loops and redundancies effectively.

Maintains linear derivations similar to Prolog.

Compatible with existing Prolog implementations.

Abstract

Infinite loops and redundant computations are long recognized open problems in Prolog. Two ways have been explored to resolve these problems: loop checking and tabling. Loop checking can cut infinite loops, but it cannot be both sound and complete even for function-free logic programs. Tabling seems to be an effective way to resolve infinite loops and redundant computations. However, existing tabulated resolutions, such as OLDT-resolution, SLG- resolution, and Tabulated SLS-resolution, are non-linear because they rely on the solution-lookup mode in formulating tabling. The principal disadvantage of non-linear resolutions is that they cannot be implemented using a simple stack-based memory structure like that in Prolog. Moreover, some strictly sequential operators such as cuts may not be handled as easily as in Prolog. In this paper, we propose a hybrid method to resolve infinite loops and redundant computations. We combine the ideas of loop checking and tabling to establish a linear tabulated resolution called TP-resolution. TP-resolution has two distinctive features: (1) It makes linear tabulated derivations in the same way as Prolog except that infinite loops are broken and redundant computations are reduced. It handles cuts as effectively as Prolog. (2) It is sound and complete for positive logic programs with the bounded-term-size property. The underlying algorithm can be implemented by an extension to any existing Prolog abstract machines such as WAM or ATOAM.