Reasoning with orders of magnitude and approximate relations

Abstract

The O[M] formalism for representing orders of magnitude and approximate relations is described, based on seven primitive relations among quantities. Along with 21 compound relations, they permit expression and solution of engineering. problems without explicit disjunction or negation. In the semantics of the relations, strict interpretation allows exact inferences, while heuristic interpretation allows inferences more aggressive and human-like but not necessarily error-free. Inference strategies within O[M] are based on propagation of order of magnitude relations through properties of the relations, solved or unsolved algebraic constraints, and rules. Assumption-based truth-maintenance is used, and the physical dimensions of quantities efficiently constrain the inferences. Statement of goals allows more effective employment of the constraints and focuses the system's opportunistic forward reasoning. Examples on the analysis of biochemical pathways are presented.