The problem of demodulation during inference rule application

Abstract

This article is the twenty-second of a series of articles discussing various open research problems in automated reasoning. The problem proposed for research asks one to find criteria for deciding when to permit and when to avoid demodulation during the application of inference rules, focusing mainly on hyperresolution, UR-resolution, and hyperparamodulation. Since these three inference rules admit natural points at which one or more demodulators (rewrite rules) could be applied-for example, after the removal of a literal or the replacement of a term-and since the dominant practice is to demodulate only after an inference rule has been completely applied, the proposed research focuses on an intriguing alternative. For evaluating a proposed solution to this research problem, we suggest problems from mathematics, logic, circuit design, program verification, and the world of puzzles.