{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T03:06:08Z","timestamp":1777431968403,"version":"3.51.4"},"reference-count":36,"publisher":"SAGE Publications","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["AO"],"published-print":{"date-parts":[[2022,8,3]]},"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.3233\/ao-220268","type":"journal-article","created":{"date-parts":[[2022,7,12]],"date-time":"2022-07-12T11:38:47Z","timestamp":1657625927000},"page":"337-364","source":"Crossref","is-referenced-by-count":4,"title":["The semantics of extensive quantities within geographic information"],"prefix":"10.1177","volume":"17","author":[{"given":"Eric","family":"Top","sequence":"first","affiliation":[{"name":"Department of Human Geography and Planning, Utrecht University, the Netherlands"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Simon","family":"Scheider","sequence":"additional","affiliation":[{"name":"Department of Human Geography and Planning, Utrecht University, the Netherlands"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haiqi","family":"Xu","sequence":"additional","affiliation":[{"name":"Department of Human Geography and Planning, Utrecht University, the Netherlands"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Enkhbold","family":"Nyamsuren","sequence":"additional","affiliation":[{"name":"Department of Human Geography and Planning, Utrecht University, the Netherlands"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Niels","family":"Steenbergen","sequence":"additional","affiliation":[{"name":"Department of Human Geography and Planning, Utrecht University, the Netherlands"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","reference":[{"issue":"3","key":"10.3233\/AO-220268_ref1","doi-asserted-by":"publisher","first-page":"313","DOI":"10.3233\/AO-200231","article-title":"The FOUnt ontologies for quantities, units, and the physical world","volume":"15","author":"Aameri","year":"2020","journal-title":"Applied Ontology"},{"issue":"5","key":"10.3233\/AO-220268_ref2","doi-asserted-by":"publisher","first-page":"501","DOI":"10.1006\/jcht.1996.0171","article-title":"Legendre transforms in chemical thermodynamics","volume":"29","author":"Alberty","year":"1997","journal-title":"The Journal of Chemical Thermodynamics"},{"key":"10.3233\/AO-220268_ref4","unstructured":"Campbell, N.R. (1920). Physics\u00a0\u2013 the Elements. Cambridge: Univ. Press."},{"key":"10.3233\/AO-220268_ref5","doi-asserted-by":"publisher","DOI":"10.1021\/ed069p957"},{"key":"10.3233\/AO-220268_ref6","doi-asserted-by":"crossref","unstructured":"Casati, R., Varzi, A.C., et al.\u00a0(1999). Parts and Places: The Structures of Spatial Representation. Mit Press.","DOI":"10.7551\/mitpress\/5253.001.0001"},{"issue":"4","key":"10.3233\/AO-220268_ref11","doi-asserted-by":"publisher","first-page":"231","DOI":"10.1559\/152304098782383043","article-title":"Rethinking levels of measurement for cartography","volume":"25","author":"Chrisman","year":"1998","journal-title":"Cartography and Geographic Information Systems"},{"key":"10.3233\/AO-220268_ref12","unstructured":"Chrisman, N.R. (2002). Exploring Geographic Information Systems. New York: Wiley."},{"issue":"4","key":"10.3233\/AO-220268_ref13","doi-asserted-by":"publisher","first-page":"411","DOI":"10.1007\/s101090100066","article-title":"An integrated representation of spatial and temporal relationships between evolving regions","volume":"3","author":"Claramunt","year":"2001","journal-title":"Journal of Geographical Systems"},{"key":"10.3233\/AO-220268_ref14","doi-asserted-by":"crossref","unstructured":"Cohen, E.R., Cvitas, T., Frey, J., Holmstrom, B., Kuchitsu, K., Marquardt, R., Mills, I., Pavese, F., Quack, M., Stohner, J., Strauss, H., Takami, M. & Thor, A.J. (2007). Quantities, Units and Symbols in Physical Chemistry. Green Book: IUPAC.","DOI":"10.1039\/9781847557889"},{"issue":"1","key":"10.3233\/AO-220268_ref17","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1080\/13658816.2019.1652304","article-title":"Fourth paradigm GIScience? Prospects for automated discovery and explanation from data","volume":"34","author":"Gahegan","year":"2020","journal-title":"International Journal of Geographical Information Science"},{"issue":"2","key":"10.3233\/AO-220268_ref18","doi-asserted-by":"publisher","first-page":"71","DOI":"10.3233\/AO-2009-0067","article-title":"The water falls but the waterfall does not fall: New perspectives on objects, processes and events","volume":"4","author":"Galton","year":"2009","journal-title":"Applied Ontology"},{"key":"10.3233\/AO-220268_ref19","unstructured":"Gangemi, A., Guarino, N., Masolo, C. & Oltramari, A. (2001). Understanding top-level ontological distinctions. In OIS@ IJCAI."},{"key":"10.3233\/AO-220268_ref21","unstructured":"Guarino, N., Welty, C., et al.\u00a0(2000). Identity, unity, and individuality: Towards a formal toolkit for ontological analysis. In ECAI (Vol.\u00a02000, pp. 219\u2013223). Citeseer."},{"key":"10.3233\/AO-220268_ref23","doi-asserted-by":"publisher","first-page":"7","DOI":"10.1111\/j.1435-5597.1970.tb01464.x","article-title":"What about people in regional science?","volume":"24","author":"H\u00e4gerstrand","year":"1970","journal-title":"Papers of the Regional Science Association"},{"key":"10.3233\/AO-220268_ref24","unstructured":"Hey, A.J., Tansley, S., Tolle, K.M., et al.\u00a0(2009). The Fourth Paradigm: Data-Intensive Scientific Discovery (Vol. 1). Redmond, WA: Microsoft Research."},{"key":"10.3233\/AO-220268_ref25","doi-asserted-by":"crossref","unstructured":"Hitzler, P., Krotzsch, M. & Rudolph, S. (2009). Foundations of Semantic Web Technologies. Chapman and Hall\/CRC.","DOI":"10.1201\/9781420090512"},{"key":"10.3233\/AO-220268_ref26","unstructured":"H\u00f6lder, O. (1901). Die Axiome der Quantit\u00e4t und die Lehre Vom Mass. Teubner."},{"key":"10.3233\/AO-220268_ref27","unstructured":"Kocourek, R.A. (2018). Quantity. New Catholic Encyclopedia. https:\/\/www.encyclopedia.com\/literature-and-arts\/language-linguistics-and-literary-terms\/language-and-linguistics\/quantity."},{"issue":"12","key":"10.3233\/AO-220268_ref28","doi-asserted-by":"publisher","first-page":"2267","DOI":"10.1080\/13658816.2012.722637","article-title":"Core concepts of spatial information for transdisciplinary research","volume":"26","author":"Kuhn","year":"2012","journal-title":"International Journal of Geographical Information Science"},{"key":"10.3233\/AO-220268_ref29","doi-asserted-by":"publisher","DOI":"10.3389\/fpsyg.2018.00522"},{"issue":"2","key":"10.3233\/AO-220268_ref30","doi-asserted-by":"publisher","first-page":"191","DOI":"10.1023\/A:1005327718934","article-title":"Entity, identity and unity","volume":"48","author":"Lowe","year":"1998","journal-title":"Erkenntnis"},{"key":"10.3233\/AO-220268_ref32","doi-asserted-by":"publisher","DOI":"10.1088\/0143-0807\/35\/3\/035017"},{"key":"10.3233\/AO-220268_ref35","doi-asserted-by":"crossref","unstructured":"Padmanabhan, R. & Rudeanu, S. (2008). Axioms for Lattices and Boolean Algebras. World Scientific.","DOI":"10.1142\/7007"},{"key":"10.3233\/AO-220268_ref36","unstructured":"Plewe, B.S. (2019). A case for geographic masses. In 14th International Conference on Spatial Information Theory (COSIT 2019). Schloss Dagstuhl-Leibniz-Zentrum Fuer Informatik."},{"issue":"1\u20132","key":"10.3233\/AO-220268_ref37","doi-asserted-by":"publisher","first-page":"63","DOI":"10.3233\/AO-2008-0046","article-title":"Observations, measurements and semantic reference spaces","volume":"3","author":"Probst","year":"2008","journal-title":"Applied Ontology"},{"key":"10.3233\/AO-220268_ref38","doi-asserted-by":"publisher","DOI":"10.1021\/ed047p154.2"},{"issue":"1","key":"10.3233\/AO-220268_ref39","doi-asserted-by":"publisher","first-page":"3","DOI":"10.3233\/SW-2012-0069","article-title":"Ontology of units of measure and related concepts","volume":"4","author":"Rijgersberg","year":"2013","journal-title":"Semantic Web"},{"issue":"1","key":"10.3233\/AO-220268_ref43","doi-asserted-by":"publisher","first-page":"28","DOI":"10.1080\/13658816.2018.1514120","article-title":"Distinguishing extensive and intensive properties for meaningful geocomputation and mapping","volume":"33","author":"Scheider","year":"2019","journal-title":"International Journal of Geographical Information Science"},{"key":"10.3233\/AO-220268_ref44","doi-asserted-by":"crossref","unstructured":"Simons, P. (2013). Density, angle, and other dimensional nonsense: How not to standardize quantity. In Johanssonian Investigations (pp. 516\u2013534). De Gruyter.","DOI":"10.1515\/9783110322507.516"},{"key":"10.3233\/AO-220268_ref45","unstructured":"Sinton, D. (1978). The inherent structure of information as a constraint to analysis: Mapped thematic data as a case study. In Harvard Papers on Geographic Information Systems."},{"key":"10.3233\/AO-220268_ref46","doi-asserted-by":"crossref","unstructured":"Steinberg, M.D., Schindler, S. & Keil, J.M. (2016). Use cases and suitability metrics for unit ontologies. In OWL: Experiences and Directions\u2013Reasoner Evaluation (pp. 40\u201354). Springer.","DOI":"10.1007\/978-3-319-54627-8_4"},{"key":"10.3233\/AO-220268_ref47","doi-asserted-by":"crossref","unstructured":"Stevens, S.S., et al.\u00a0(1946). On the Theory of Scales of Measurement.","DOI":"10.1126\/science.103.2684.677"},{"key":"10.3233\/AO-220268_ref48","unstructured":"Suppes, P. & Zinnes, J.L. (1962). Basic measurement theory. In Handbook of Mathematical Psychology (Vol.\u00a01)."},{"issue":"3","key":"10.3233\/AO-220268_ref50","first-page":"237","article-title":"The measurable quantities of physics","volume":"9","author":"Tolman","year":"1917","journal-title":"Physical Review"},{"issue":"1","key":"10.3233\/AO-220268_ref51","doi-asserted-by":"publisher","first-page":"52","DOI":"10.2307\/211729","article-title":"\u201cCrossbreeding\u201d geographical quantities","volume":"45","author":"Wright","year":"1955","journal-title":"Geographical Review"},{"key":"10.3233\/AO-220268_ref52","first-page":"1","article-title":"Extracting interrogative intents and concepts from geo-analytic questions","volume":"1","author":"Xu","year":"2020","journal-title":"AGILE: GIScience Series"}],"container-title":["Applied Ontology"],"original-title":[],"link":[{"URL":"https:\/\/content.iospress.com\/download?id=10.3233\/AO-220268","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T11:46:23Z","timestamp":1777376783000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/full\/10.3233\/AO-220268"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,8,3]]},"references-count":36,"journal-issue":{"issue":"3"},"URL":"https:\/\/doi.org\/10.3233\/ao-220268","relation":{},"ISSN":["1875-8533","1570-5838"],"issn-type":[{"value":"1875-8533","type":"electronic"},{"value":"1570-5838","type":"print"}],"subject":[],"published":{"date-parts":[[2022,8,3]]}}}