Geographic information reflects ontological world views, just like any linguistic utterance. However, in comparison with spoken language, all kinds of digital information is affected by the problem of reference to an even larger extent, because of the loss of the context of speech. How can the phenomena underlying digital information be referred to in an inter-subjective way? The problem is not that machines cannot communicate, but that humans frequently misunderstand each other when communicating via machines. This book puts forward a (...) proposal about how semantic reference can be reproduced based on the operations necessary to generate a dataset. These include cognitive constructions as well as perceptual operations, i. e., operations of the human attentional apparatus. Perceptual operations allow one to share information by focusing human attention on aeGestaltsAE in the perceived space around the body. Gestalt mechanisms allow observers to make predications, i. e., to relate foci of attention. The author proposes a kind of aepractical constructivismAE guided by a formal language.The idea is to describe data aebottom-upAE in order to reconstruct the observation and abstraction process, instead of presuming abstract ontological concepts. This approach is demonstrated by reconstructing the concept of a road network, which underlies an important kind of geographic data. (shrink)

The next generation of Geographic Information Systems 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. (shrink)