A theory of interactions: unifying qualitative and quantitative algebraic reasoning

摘要

The apparently weak properties of a purely qualitative algebra have led some to conclude that researchers must turn instead to extra-mathematical properties of physical systems. We propose instead that a more powerful qualitative algebra is needed, one that merges the algebras on signs and reals, along with symbolic techniques for manipulating this algebra. We have constructed a hybrid algebra, called SR1 which allows intermediate abstractions to be selected between traditional qualitative and quantitative algebras.