Order-of-magnitude reasoning with O[M]

The O[M] formalism for Order-of-Magnitude reasoning is described. O[M] is based on seven primitive relations among absolute magnitudes of quantities: 'much less than' (< <), 'moderately less than' (- <), 'slightly less than' (∼ <), 'equal to' (= =), 'slightly greater than' (> ∼), 'moderately greater than' (> -), and 'much greater than' (> >). 21 compound relations are formed as implicit disjunctions of consecutive primitive relations. A strict interpretation of the relations allows exact conservative inferences, while a heuristic interpretation allows more aggressive and human-like inferences, by permitting some slack at each inference step. Inference strategies are based on propagation of order-of-magnitude relations through properties of the relations, algebraic constraints, and rules. O[M] operates mainly in the data-driven direction with assumption-based truth-maintenance for the resolution of contradictions. O[M] provides efficient integration of quantitative and qualitative knowledge in the expression and solution of engineering problems. The system has been applied in process engineering and biochemical engineering.