A congnitive model of axiom formulation and reformulation with application to AI and software engineering

  • Smaill, Alan (Principal Investigator)
  • Clark, Andy (Co-investigator)

Project Details


The project was concerned to build models of the process of building
axiomatisations of mathematical theories, building on notions of mathematical
analogy and transfer. This leads to a marriage between the formalisms
of institution theory and information flow, and the cognitive claims of
Lakoff and Nunez on the formation of mathematical ideas. Lakatos's ideas
on the evolution of mathematical theories was also a strong influence.

Layman's description

Reasoning by analogy between different areas has been a tool in the invention
of scientific theories for a long time, eg "the atom is like the solar system" --
in that electrons/planets are attracted to and move round a central attractor.
The project looked at the role of mathematical analogy -- both analogies
between everyday tasks like measuring and mathematical notions of number;
and analogies between mathematical theories that are already developed.
This opens up new possibilities in creative interactions between computers,
mathematicians, and learners who can explore the possible changes
and variations in inventing and merging new forms of mathematical thinking.

Key findings

It is possible to build computer models of the understanding of mathematical
domains that reflect both mathematical accuracy, and different particular
ways in which the mathematics reflects individual experience.
For example, there are different notions of number that arise from
different experiences, such as using a measuring stick or looking
at motion long a path; and these ideas come together in notions of
number that developed over a long period.
These models allow computer support for combining such different ideas,
and helping people explore the different ways new mathematical notions
can be formulated, based on existing notions and on new examples, which
suggest new ways of thinking.
Effective start/end date1/05/0830/04/11


  • EPSRC: £642,560.00


Explore the research topics touched on by this project. These labels are generated based on the underlying awards/grants. Together they form a unique fingerprint.
  • Utility-Based Generation of Referring Expressions

    Guhe, M., Apr 2012, In: Topics in Cognitive Science. 4, 2, p. 306-329 24 p.

    Research output: Contribution to journalArticlepeer-review

  • Towards a cognitive model of conceptual blending

    Guhe, M., Smaill, A. & Pease, A., 5 Aug 2010, Proceedings of the 10th International Conference on Cognitive Modeling. p. 293-304 12 p.

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Open Access
  • Mathematical reasoning with higher-order anti-unifcation

    Guhe, M., Pease, A., Smaill, A., Schmidt, M., Gust, H., Kühnberger, K-U. & Krumnack, U., 2010, Proceedings of the 32nd Annual Conference of the Cognitive Science Society. p. 1992-1997 6 p.

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Open Access