The Semantics of Extensive Quantities in Geographical Information

Abstract

The next generation of Geographical Information Systems (GIS) is anticipated to automate some ofthe reasoning required for spatial analysis. An important step in the development of such systems is abetter understanding and modeling of the decision process about which arithmetic operations can bemeaningfully applied to geographic quantities. The concept of extensivity plays an important role indetermining precisely what amounts are, when they can be aggregated by summing them, and whenthis is not possible. However, currently, multiple contrasting definitions of extensivity exist, andnone of these suffice for handling the different practical cases occurring in geographical information.As a result, GI-analysts predominantly rely on intuition and ad hoc reasoning to determine whethertwo quantities are additive. In this paper, we present a novel approach to formalizing the conceptof extensivity. In our algebraic definition, we do away with some of the constraints that limit theuse of older approaches. By treating extensivity as a relation between quantities, our definitionoffers the flexibility to relate a quantity to many domains of interest. We show how this new notionof extensivity can be used to classify the kinds of amounts in various examples of geographicalinformation.