2026-09-10T09:45:00Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:27546 2026-09-10T05:38:42Z ddc:004 open_access

When Are Geographic Quantities Semantically Compatible with Each Other?: Towards a Constructive Theory of Amounts, Magnitudes, and Proportions Scheider, Simon Wang, Shuai Top, Eric geographic quantities semantics of measurement GIS geodata repositories 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Simon Scheider and Shuai Wang and Eric Top 2026 Is Part Of LIPIcs, Volume 393, 17th International Conference on Spatial Information Theory (COSIT 2026) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.COSIT.2026.2 urn:nbn:de:0030-drops-275464 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.COSIT.2026.2 eng https://creativecommons.org/licenses/by/4.0/legalcode