A theory of interactions: Unifying qualitative and quantitative algebraic reasoning
In order to develop a model-based theory of design for continuous, lumped parameter devices, the author proposed three hybrid algebras that capture qualitative and quantitative information about interactions and implemented a qualitative symbolic algebra system, called Minima, that provides improved facilities for composing and comparing equations. The paper concentrates on the SR1 hybrid algebra, that merges the signs and reals into a single domain, on its expressive power, as well as the capacity of SR1 and Minima: (1) to select the right level of abstraction; and (2) to efficiently combine qualitative and quantitative reasoning. This is achieved by embodying: a weaker relation of qualitative equality, substitution of equals, qualitative composition and hybrid resolution, inference rules needed for design and verification, qualitative arithmetic reasoning, composition of monotonicity relations etc. Implemented on a Symbolics 3600 (using Symbolics and DOE Macsyma), the Minima system (and SR1 algebra) demonstrated a progress in the design of a better theory of interactions, and proved to be useful in a variety of fluid regulation devices.
scientific article; zbMATH DE number 55598