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Erschienen in:
2016 | OriginalPaper | Buchkapitel
A Generic Approach to Diagrammatic Representation: The Case of Single Feature Indicator Systems
verfasst von : Atsushi Shimojima, Dave Barker-Plummer
Erschienen in: Diagrammatic Representation and Inference
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Abstract
In this paper we take a generic approach to developing a theory of representation systems. Our approach involves giving an abstract formal characterization of a class of representation systems, and proving formal results based on this characterization.
We illustrate this approach by defining and investigating two closely related classes of representations that we call Single Feature Indicator Systems (SFIS), with and without neutrality. Many common representations including tables, such as timetables and work schedules; connectivity graphs, including route maps and circuit diagrams; and statistical charts such as bar graphs, either are SFIS or contain one as a component.
By describing SFIS abstractly, we are able to prove some properties of all of these representation systems by virtue of the fact that the properties can be proved on the basis of the abstract definition only. In particular we show that certain abstract inference rules are sound, and that each instance admits concrete inference rules obtained by instantiating the abstract counterparts.