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DOI: 10.4230/LIPIcs.COSIT.2026.2
When Are Geographic Quantities Semantically Compatible with Each Other?: Towards a Constructive Theory of Amounts, Magnitudes, and Proportions

Authors: Simon Scheider, Shuai Wang, and Eric Top

Published in: LIPIcs, Volume 393, 17th International Conference on Spatial Information Theory (COSIT 2026)

Abstract
Geographic quantities are more than just numbers. A particular semantics is required to interpret them, which is best captured by constructive types. From a practical viewpoint, numerical operations are only applicable to certain types of geographic quantities, while for others, they become meaningless, even if they are numerically well-defined. For example, GIS experts know that it is meaningless to multiply some quantities - measured, for instance, in people or square kilometers - with one another. In contrast, areas can meaningfully be multiplied by population densities to obtain the number of people living in that area. We currently lack a semantic theory that allows us to determine whether quantities represented in geodata models are compatible with one another for deriving new quantities by common GIS operations. In this paper, we distinguish three distinct types of quantities that are often collapsed into numbers: amounts, magnitudes, and proportions. For each type, we introduce a constructive first-order logic theory. We then define quantifiable experiments represented by different data sources drawn from a geodata repository, and apply the theory to determine the compatibility of those sources for deriving new quantities.
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Simon Scheider, Shuai Wang, and Eric Top. When Are Geographic Quantities Semantically Compatible with Each Other?: Towards a Constructive Theory of Amounts, Magnitudes, and Proportions. In 17th International Conference on Spatial Information Theory (COSIT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 393, pp. 2:1-2:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{scheider_et_al:LIPIcs.COSIT.2026.2,
  author =	{Scheider, Simon and Wang, Shuai and Top, Eric},
  title =	{{When Are Geographic Quantities Semantically Compatible with Each Other?: Towards a Constructive Theory of Amounts, Magnitudes, and Proportions}},
  booktitle =	{17th International Conference on Spatial Information Theory (COSIT 2026)},
  pages =	{2:1--2:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-438-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{393},
  editor =	{Timpf, Sabine and Filomena, Gabriele and Kapaj, Armand and Zhu, Rui and Giudice, Nicholas A. and Manley, Ed},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.COSIT.2026.2},
  URN =		{urn:nbn:de:0030-drops-275464},
  doi =		{10.4230/LIPIcs.COSIT.2026.2},
  annote =	{Keywords: geographic quantities, semantics of measurement, GIS, geodata repositories}
}

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