Abstract
We present a novel framework for inspecting representations and encoding their formal properties. This enables us to assess and compare the informational and cognitive value of different representations for reasoning. The purpose of our framework is to automate the process of representation selection, taking into account the candidate representation’s match to the problem at hand and to the user’s specific cognitive profile. This requires a language for talking about representations, and methods for analysing their relative advantages. This foundational work is first to devise a computational end-to-end framework where problems, representations, and user’s profiles can be described and analysed. As AI systems become ubiquitous, it is important for them to be more compatible with human reasoning, and our framework enables just that.
This work was supported by the EPSRC Grants EP/R030650/1 and EP/R030642/1.
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Notes
- 1.
As a consequence, Q tables may contain elements of multiple RSs. For reasons mentioned in Sect. 5, this is discouraged whenever it is avoidable.
- 2.
Those appearing in this example are taken from a semantic net [29].
- 3.
In future work, we will investigate how correspondences and their strength can be identified automatically (e.g., using machine learning).
- 4.
By ‘Euler’ we mean some implementation of Euler diagrams.
- 5.
and requires that both properties appear in the property table. or requires that at least one of the properties appears in the property table. If both properties appear in the table, the strength is only counted once. not requires that a specified property does not occur in the property table.
- 6.
The value 0.6 for ‘instrumental’ properties is chosen arbitrarily; the only condition is that the value-importance relation is monotonic. In future work, these parameters should be tuned with experimental data.
- 7.
In Euler diagrams the cardinality of sets is abstracted away; the size of zones is meaningless.
- 8.
Note that the strength of the correspondences from probability to \(\Pr \) and compare sizes was set to 1 (because in principle any probability function is representable in the Bayesian or Geometric systems), but it was set to 0.5 for Contingency because not every probability function is representable in Contingency tables.
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We thank the 3 anonymous reviewers for their comments, which helped to improve the presentation of this paper.
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Raggi, D., Stockdill, A., Jamnik, M., Garcia Garcia, G., Sutherland, H.E.A., Cheng, P.CH. (2019). Inspection and Selection of Representations. In: Kaliszyk, C., Brady, E., Kohlhase, A., Sacerdoti Coen, C. (eds) Intelligent Computer Mathematics. CICM 2019. Lecture Notes in Computer Science(), vol 11617. Springer, Cham. https://doi.org/10.1007/978-3-030-23250-4_16
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