A Theory of Justified Reformulations

Abstract

Present day systems, intelligent or otherwise, are limited by the conceptualizations of the world given to them by their designers. In this paper, we propose a novel, first-principles approach to performing incremental reformulations for computational efficiency. First, we define a reformulation to be a shift in conceptualization: a change in the basic objects, functions, and relations assumed in a formulation. We then analyze the requirements for automating reformulation and show the need for justifying shifts in conceptualization.

Inefficient formulations make irrelevant distinctions. A new class of meta-theoretical justifications for a reformulation called irrelevance explanations, is presented. A logical irrelevance explanation demonstrates that certain distinctions made in the formulation are not necessary for the computation of a given class of problems. A computational irrelevance explanation shows that some distinctions are not useful with respect to a given problem solver for a given class of problems. We then present a meta-theoretical principle of ontological economy called the irrelevance principle. The irrelevance principle logically minimizes a formulation by removing all facts and distinctions that are either logically or computationally irrelevant to the specified goals. The automation of the irrelevance principle is demonstrated with an example from the world of kinship. We also describe the implementation of an irrelevance reformulator and outline preliminary experimental results that confirm our theory.