The Semantics of Extensive Quantities within Geographic Information

Eric Top*, Simon Scheider, Enkhbold Nyamsuren, Haiqi Xu, Niels Steenbergen

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review


The next generation of Geographic Information Systems (GIS) is anticipated to automate some of the reasoning required for spatial analysis. An important step in the development of such systems is to gain a better understanding and corresponding modeling practice of when to apply arithmetic operations to quantities. The concept of extensivity plays an essential role in determining when quantities can be aggregated by summing them, and when this is not possible. This is of particular importance to geographic information systems, which serve to quantify phenomena across space and time. However, currently, multiple contrasting definitions of extensivity exist, and none of these suffice for handling the different practical cases occurring in geographic information. As a result, analysts predominantly rely on intuition and ad hoc reasoning to determine whether two quantities are additive. In this paper, we present a novel approach to formalizing the concept of extensivity. Though our notion as such is not restricted to quantifications occurring within geographic information, it is particularly useful for this purpose. Following the idea of spatio-temporal controls by Sinton, we define extensivity as a property of measurements of quantities with respect to a controlling quantity, such that a sum of the latter implies a sum of the former. In our algebraic definition of amounts and other quantities, we do away with some of the constraints that limit the usability of older approaches. By treating extensivity as a relation between amounts and other types of quantities, our definition offers the flexibility to relate a quantity to many domains of interest. We show how this new notion of extensivity can be used to classify the kinds of amounts in various examples of geographic information.
Original languageEnglish
Article number3
Pages (from-to)337-364
Number of pages28
JournalApplied Ontology
Issue number3
Publication statusPublished - 3 Aug 2022


  • Extensive quantities
  • definition
  • geocomputation
  • semantic labeling of geodata


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