Abstract
We present a framework for assessing the relative cognitive cost of different representational systems for problem solving. The framework consists of 13 cognitive properties. These properties are mapped according to two dimensions: (1) the time scale of the cognitive process, and (2) the granularity of the representational system. The work includes analyses of those processes that are relevant to the internal mental world, and those that are relevant to the external physical display too. The motivation for the construction of this framework is to support the engineering of an automated system that (a) selects representations, (b) that are suited for individual users, (c) and works on specific classes of problems. We present a prototype implementation of such an automated representation selection system, along with an evaluation.
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Notes
- 1.
Following [18], a representational system is an abstract entity from which many distinct individual representations may be created.
- 2.
Following [27], ERs are information and objects that exist in the external environment and can be perceived; while IRs are knowledge and structures in memory (p. 180).
- 3.
Across disciplines, different terminology is used for symbols and expressions. From a computational perspective, [18] refers to primitives instead of symbols, and composites instead of expressions. These differences partially rise from different perspectives on what is understood by a basic/elementary unit, whether it is considered decomposable or not. As this paper focuses on cognitive aspects of RSs, we have adopted cognitive-oriented terminology.
- 4.
In formal, sentential mathematics these would be called axioms, but we do not want to give the impression that either (i) our system only applies to axiomatic systems or that (ii) laws have to be as low level as axioms typically are.
- 5.
Other CPs, e.g., IR & ER-semantic-process and solution-technique, are yet to be implemented.
- 6.
Information suitability measures how well a representation encodes the informational content of a problem and is computed using the formal properties of representations.
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Acknowledgements
We thank Gem Stapleton, from Cambridge University, for her comments and suggestions for this paper. This work was supported by the EPSRC grants EP/R030650/1, EP/T019603/1, EP/R030642/1, and EP/T019034/1.
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Cheng, P.CH., Garcia Garcia, G., Raggi, D., Stockdill, A., Jamnik, M. (2021). Cognitive Properties of Representations: A Framework. In: Basu, A., Stapleton, G., Linker, S., Legg, C., Manalo, E., Viana, P. (eds) Diagrammatic Representation and Inference. Diagrams 2021. Lecture Notes in Computer Science(), vol 12909. Springer, Cham. https://doi.org/10.1007/978-3-030-86062-2_43
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