Prolegomena to any Future Qualitative Physics

Abstract:

We evaluate the success of the qualitative physics enterprise in
automating expert reasoning about physical systems. The field 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 differential equations
containing unspecified 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 field has
developed several reasoners based on these choices over some fifteen
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.