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Extensivity triangle, showing possibilities of extensive measurement functions between three categories of quantity domains.

Extensivity triangle, showing possibilities of extensive measurement functions between three categories of quantity domains.

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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...

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... quantity domains that act as controls and measures. Using the two triads of SpaceAmountD, TimeAmountD and ContentAmountD, and SizeMagnitudeD, DurationMagnitudeD, and ValueMagnitudeD, a total of twelve measurement function classes can be distinguished, where each measurement function class is represented as an arrow between domain categories in Fig. 3. Three measurement function classes map from amount domains to magnitude domains within the category time, space, or content, six map between amount domains of different categories and three functions are automorphisms on three types of amount domains. In the following, we discuss each of the measurement function classes using examples ...

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... Such knowledge is needed not only for modelling geographic information concepts [12,25], and for making opaque models transparent [31], but also for understanding what kind of intelligence is needed to refer to place [9,13,18] and to handle geographic space [19,24]. Among others, researchers are currently working on formal theories of space [1] and geographic quantities [28]. Understood in this broader sense, namely as the intelligence needed to handle geographic information, geoAI has the potential to fundamentally improve the way geographic information can be processed and interpreted by both humans and machines. ...
... Yet whether a map can be interpreted in this way is neither contained in the data nor is it generally known (and thus could be retrieved [71]. At the same time, conceptualisations of geographic quantities [80] inform us that aggregations cannot be counts or densities of objects, but should be field integrals or field coverages, measuring the area covered by some interval over the noise field [71] (cf. dotted boxes in Fig. 3). ...
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Current artificial intelligence (AI) approaches to handle geographic information (GI) reveal a fatal blindness for the information practices of exactly those sciences whose methodological agendas are taken over with earth-shattering speed. At the same time, there is an apparent inability to remove the human from the loop, despite repeated efforts. Even though there is no question that deep learning has a large potential, for example, for automating classification methods in remote sensing or geocoding of text, current approaches to GeoAI frequently fail to deal with the pragmatic basis of spatial information, including the various practices of data generation, conceptualization and use according to some purpose. We argue that this failure is a direct consequence of a predominance of structuralist ideas about information. Structuralism is inherently blind for purposes of any spatial representation, and therefore fails to account for the intelligence required to deal with geographic information. A pragmatic turn in GeoAI is required to overcome this problem.