Integrating quantitative and qualitative discovery in the ABACUS system

Abstract

Most research on inductive learning has been concerned with qualitative learning that induces conceptual, logic-style descriptions from the given facts. In contrast, quantitative learning deals with discovering numerical laws characterizing empirical data. This research attempts to integrate both types of learning by combining newly developed heuristics for formulating equations with the previously developed concept learning method embodied in the inductive learning program AQ11. The resulting system, ABACUS, formulates equations that bind subsets of observed data, and derives explicit, logic-style descriptions stating the applicability conditions for these equations. In addition, several new techniques for quantitative learning are introduced. Units analysis reduces the search space of equations by examining the compatibility of variables' units. Proportionality graph search addresses the problem of identifying relevant variables that should enter equations. Suspension search focusses the search space through heuristic evaluation. The capabilities of ABACUS are demonstrated by several examples from physics and chemistry.