A Generic Approach to Diagrammatic Representation: The Case of Single Feature Indicator Systems
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.
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Faculty of Culture and Information Science, Doshisha University, 1-3 Tatara-Miyakodani, Kyotanabe 610-0394, Japan [email protected] 2 CSLI/Stanford University, Cordura Hall, 210 Panama Street, Stanford, CA 94305, USA [email protected]
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.
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Introduction
In this paper we adopt a generic approach to developing a theory of representation systems in general, with diagrammatic systems as a special case. Our approach involves giving an abstract formal characterization of a class of representation systems, and then proving results about the properties of all members of the class in the abstract setting. By adopting this approach, we are able to short-circuit investigation of individual representation systems, and also to assign the responsibility for the possession of various properties of an individual representation system to its membership in the class. Specifically, we do three things in this paper: 1. Describe and formalize our view of a representation system. Our formalization uses channel theory, a formal framework for modeling information c Springer International Publishing Switzerland 2016 M. Jamnik et al. (Eds.): Diagrams 2016, LNAI 9781, pp. 83–97, 2016. DOI: 10.1007/978-3-319-42333-3 7
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A. Shimojima and D. Barker-Plummer
flow, of which representation is a special case [3]. This task occupies Sects. 2 and 3 of this paper. 2. Show how to model particular types of representation systems within the channel theory framework. We focus on two closely related classes of representation systems: Single Feature Indicator Systems with and without neutrality (SFIS). This is the content of Sects. 4 and 5. SFISs are among the simplest representation systems that we can think of, and are built into a number of important, familiar diagrammatic representation systems. Each of the diagrams presented in Fig. 1 illustrates a system that either is an SFIS itself or has an SFIS as its main component. We will refer to these examples throughout this paper. 3. Demonstrate prope
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