Qualitative Reasoning with Spatially Distributed Parameters

This paper presents work on modelling the qualitative behaviour of physical systems of spatially distributed parameters. The distribution of each parameter is given as a set of observation points. A metric diagram is constructed by defining a connectivity structure on the point set. The metric diagram is used to construct a topological map that represents the distribution of the parameter as a pattern of contiguous regions. The regions represent values in the l)arameter’s quantity space, which is a discretization of its value domain. Topological combinations of parameter distributions are used to infer the distributions of nonobserved parameters according to models of parameter correspondences, e.g. qualitative versions of equations. The spatial evolution of the system is inferred by matching the scenario’s parameter patterns against modelled patterns of physical processes. The al)proach is suitable for modelling common-sense reasoning in the natural sciences, e.g. meteorology, agriculture, climate studies and natural resource management.