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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsNotes
- 1.
We sometime call this the core theory, hence the subscript “c”.
References
Barker-Plummer, D., Etchemendy, J., Murray, M., Pease, E., Swoboda, N.: Learning to use the openbox: a framework for the implementation of heterogeneous reasoning. In: Cox, P., Plimmer, B., Rodgers, P. (eds.) Diagrams 2012. LNCS, vol. 7352, pp. 3–3. Springer, Heidelberg (2012)
Barwise, J., Etchemendy, J.: Hyperproof. CSLI Publications, Stanford (1994)
Barwise, J., Seligman, J.: Information Flow: The Logic of Distributed Systems. Cambridge University Press, Cambridge (1997)
Jamnik, M.: Mathematical Reasoning with Diagrams. CSLI Publications, Stanford (2001)
Miller, N.: Euclid and His Twentieth Century Rivals: Diagrams in the Logic of Euclidean Geometry. CSLI Publications, Stanford (2007)
Shimojima, A.: Semantic Properties of Diagrams and Their Cognitive Potentials. Studies in the Theory and Applications of Diagrams. CSLI Publications, Stanford (2015)
Urbas, M., Jamnik, M.: A framework for heterogeneous reasoning in formal and informal domains. In: Dwyer, T., Purchase, H., Delaney, A. (eds.) Diagrams 2014. LNCS, vol. 8578, pp. 277–292. Springer, Heidelberg (2014)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this paper
Cite this paper
Shimojima, A., Barker-Plummer, D. (2016). A Generic Approach to Diagrammatic Representation: The Case of Single Feature Indicator Systems. In: Jamnik, M., Uesaka, Y., Elzer Schwartz, S. (eds) Diagrammatic Representation and Inference. Diagrams 2016. Lecture Notes in Computer Science(), vol 9781. Springer, Cham. https://doi.org/10.1007/978-3-319-42333-3_7
Download citation
DOI: https://doi.org/10.1007/978-3-319-42333-3_7
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-42332-6
Online ISBN: 978-3-319-42333-3
eBook Packages: Computer ScienceComputer Science (R0)