Termination Proofs for Logic Programs with Tabling

TL;DR

This paper introduces new notions of universal termination for logic programs with tabling, providing sufficient and necessary conditions, modular proofs, and automatic methods for termination analysis.

Contribution

It defines quasi-termination and LG-termination, offers conditions for these, and develops modular and automatic proof techniques for termination in logic programming with tabling.

Findings

Established sufficient conditions for quasi-termination and LG-termination.

Provided necessary conditions for well-chosen tabling.

Developed modular and automatic termination proof methods.

Abstract

Tabled logic programming is receiving increasing attention in the Logic Programming community. It avoids many of the shortcomings of SLD execution and provides a more flexible and often extremely efficient execution mechanism for logic programs. In particular, tabled execution of logic programs terminates more often than execution based on SLD-resolution. In this article, we introduce two notions of universal termination of logic programming with Tabling: quasi-termination and (the stronger notion of) LG-termination. We present sufficient conditions for these two notions of termination, namely quasi-acceptability and LG-acceptability, and we show that these conditions are also necessary in case the tabling is well-chosen. Starting from these conditions, we give modular termination proofs, i.e., proofs capable of combining termination proofs of separate programs to obtain termination proofs of combined programs. Finally, in the presence of mode information, we state sufficient conditions which form the basis for automatically proving termination in a constraint-based way.