Department of Computer Science and Technology

Technical reports

Automating representation change across domains for reasoning

Aaron Stockdill

June 2022, 268 pages

This technical report is based on a dissertation submitted September 2021 by the author for the degree of Doctor of Philosophy to the University of Cambridge, Selwyn College.

DOI: 10.48456/tr-971


Representing a problem well can make it trivial to solve; represent it poorly, and it becomes impossible. But what makes a representation suitable for a problem, and how can we automatically choose the most suitable from a set of alternatives? Choosing an appropriate representation is a difficult, long-standing problem in artificial intelligence; we want to support people in making an appropriate representation selection based on the problem they are solving, their own cognitive strengths, and the representational systems available. A large part of the challenge in choosing alternative representations stems from not knowing what is ‘the same’: which parts in the problem statement correspond to parts of an analogous statement in a different representation. If instead this choice was automated, users could better understand the problem, and work towards a solution when given a more appropriate representation.

This dissertation contributes a novel approach for the identification of alternative representations of problems through the idea of correspondences. This is a key step towards being able to select representations that are well-suited to enabling problem solutions. Exploiting correspondences, we demonstrate how to compute the informational suitability of alternative representational systems; the practical utility of this is shown with a software implementation. The generality of this theory and implementation is demonstrated by applying both to a domain that is distinct from the one it was developed in. We evaluate our theory and implementation with an empirical study, where we present experts with a similar challenge of evaluating representational system suitability, and comparing their responses with that of our implementation.

The work described in this dissertation creates possibilities for software tools that react to the problem and user: intelligent tutoring systems with multiple ways of explaining concepts to students; or interactive theorem provers that create analogies to help the human prover in finding key insights. The resulting tools centre on the representational needs of the human, not the computer.

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BibTeX record

  author =	 {Stockdill, Aaron},
  title = 	 {{Automating representation change across domains for
  year = 	 2022,
  month = 	 jun,
  url = 	 {},
  institution =  {University of Cambridge, Computer Laboratory},
  doi = 	 {10.48456/tr-971},
  number = 	 {UCAM-CL-TR-971}