Qualitative Reasoning with Spatially Distributed Parameters

This paperpresentswork on modellingthe qualitative behaviourof physical systemsof spatially distributedparameters.The distribution of each parameteris given asa set of observationpoints. A metricdiagramis constructedby definingaconnectivity structureon the point set. The metric diagram is used to constructa topological map that representsthe distribution of the parameter as a pattern of contiguousregions. The regionsrepresentvaluesin the l)arameter’squantity space,which is adiscretizationof its valuedomain. Topological combinationsof parameterdistributions are used to infer the distributions of nonobservedparametersaccordingto modelsof parametercorrespondences, e.g. qualitativeversions of equations. The spatial evolution of the system is inferredby matchingthe scenario’sparameterpatternsagainstmodelledpatternsof physical processes.The al)proachis suitablefor modelling common-sensereasoningin the natural sciences, e.g. meteorology,agriculture,climate studiesand naturalresourcemanagement.