Prolegomena to Any Future Qualitative Physics

We evaluate the success of the qualitative physics enterprise in automating expert reasoning about physical systems. The eld has agreed, in essentials, upon a modeling language for dynamical systems, a representation for behavior, and an analysis method. The modeling language consists of generalized ordinary diierential equations containing unspeciied constants and monotonic functions; the behavioral representation decomposes the state space described by the equations into discrete cells; and the analysis method traces the transitory response using sign arithmetic and calculus. The eld has developed several reasoners based on these choices over some fteen years. We demonstrate that these reasoners exhibit severe limitations in comparison with experts and can analyze only a handful of simple systems. We trace the limitations to inappropriate assumptions about expert needs and methods. Experts ordinarily seek to determine asymptotic behavior rather than transient response, and use extensive mathematical knowledge and numerical analysis to derive this information. Standard mathematics provides complete qualitative understanding of many systems, including those addressed so far in qualitative physics. Preliminary evidence suggests that expert knowledge and reasoning methods can be automated directly, without restriction to the accepted language, representation and algorithm. We conclude that expert knowledge and methods provide the most promising basis for automating qualitative reasoning about physical systems.