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2015 | OriginalPaper | Chapter

Outline of a Formal Theory of Processes and Events, and Why GIScience Needs One

Author : Antony Galton

Published in: Spatial Information Theory

Publisher: Springer International Publishing

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Abstract

It has often been noted that traditional GIScience, with its focus on data-modelling functions such as the input, storage, retrieval, organisation, manipulation, and presentation of data, cannot readily accommodate the process-modelling functions such as explanation, prediction, and simulation which it is increasingly acknowledged should form an essential element of the GI scientist’s toolkit. Although there are doubtless many different reasons for this seeming incompatibility, this paper singles out for consideration the different views of time presupposed by the two kinds of function: on the one hand, the ‘frozen’ historical time required by data modelling, and on the other, the ‘fluid’ experiential time required by process modelling. Whereas the former places an emphasis on events as discrete completed wholes, the latter is concerned with on-going continuous processes as they evolve from moment to moment. In order to reconcile the data-modelling and process-modelling requirements of GIScience, therefore, a formal theory of processes and events is developed, within which their fundamental properties can be made explicit independently of any specific implementation context, and their relationships systematically investigated.

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The term ‘analysis’ could perhaps be included with the second set of functions as well: it is a broad term which covers a range of different activities. However, many traditional GIS functions such as interpolation, overlay, and generalisation are often described as ‘analytical’, and many, though not all, of the functions described by O’Sullivan and Unwin in their book on Geographic Information Analysis [23] belong with the ‘traditional GIS functions’ rather than the ‘more advanced capabilities’.

In some more recent treatments, place and time are amalgamated, and the nature of the theme is made more explicit, as in the geo-atom of Goodchild et al., which takes the form \(\langle \mathbf{x},Z,z(\mathbf{x})\rangle \), where ‘\(\mathbf x\) defines a point in space-time, Z identifies a property, and \(z(\mathbf{x})\) defines the particular value of the property at that point’ [18].

Cf. [10]: ‘An event is an individual episode with a definite beginning and end ...’.

These are similar to what Aitken and Curtis [3] call Scripts: ‘A Script is a typical pattern of events that can be expected to re-occur: “dining in a restaurant” and “brushing one’s teeth” being well known examples’ (the restaurant example comes from the original exposition of the Script concept by Shank and Abelson [27]).

Cf. [33]: ‘[C]omputational processes are rather like computer programs, which when executed result in occurrents’. Here it is the program execution itself that is described as an occurrent, not the outputs resulting from it.

In [14], these are called ‘open’ and ‘closed’ processes respectively.

Note: This must be construed carefully: it is the type of event that is repeated, each individual event occurs just once.

It is instructive in this connection to compare Fig. 2 in [21] with Fig. 1 in [35], focussing particularly on the role assigned to the term ‘Event’ in the two diagrams.

It is important to note that the general theory has to handle event-types rather than specific unique occurrences. In defining what is meant by a chunk of some process, for example, we are characterising a type of event, not an individual event. There may be many different individual occurrences which come under this description (or only one, or none), whereas an individual event is by nature unique. If we say ‘It happened twice’ or ‘It happened again’, by ‘it’ we can only mean an event-type, of which we are reporting another occurrence.

As distinct from ‘globally finite’, which would mean there is a time before which the process is never active, and a time after which it is never active.

I have not proved this; it is a conjecture based on experiments with a number of plausible candidate definitions.

The first conjunct of the definiens is required to ensure that chunk(P) satisfies AxOcc.

The legitimacy of this definition depends on the fact, easily proved, that dechunk(E), so defined, satisfies AxAct.

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Title: Outline of a Formal Theory of Processes and Events, and Why GIScience Needs One
Author: Antony Galton
Publisher: Springer International Publishing
Book: Spatial Information Theory
Print ISBN: 978-3-319-23373-4

Electronic ISBN: 978-3-319-23374-1

Copyright Year: 2015
DOI: https://doi.org/10.1007/978-3-319-23374-1_1

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