A computational account of conceptual blending in basic mathematics

Markus Guhe, Alison Pease, Alan Smaill, Maricarmen Martinez, Martin Schmidt, Helmar Gust, Kai-Uwe Kuhnberger

Research output: Contribution to journalArticlepeer-review


We present an account of a process by which different conceptualisations of number can be blended together to form new conceptualisations via recognition of common features, and judicious combination of their distinctive features. The accounts of number are based on Lakoff and Núñez's cognitively-based grounding metaphors for arithmetic. The approach incorporates elements of analogical inference into a generalised framework of conceptual blending, using some ideas from the work of Goguen. The ideas are worked out using Heuristic-Driven Theory Projection (HDTP, a method based on higher-order anti-unification). HDTP provides generalisations between domains, giving a crucial step in the process of finding commonalities between theories. In addition to generalisations, HDTP can also transfer concepts from one domain to another, allowing the construction of new conceptual blends. Alongside the methods by which conceptual blends may be constructed, we provide heuristics to guide this process.
Original languageEnglish
Pages (from-to)249-265
Number of pages17
JournalCognitive Systems Research
Issue number3-4
Publication statusPublished - Sep 2011


  • Mathematical cognition
  • Metaphor
  • Mathematical reasoning
  • Analogy
  • Anti-unification
  • Conceptual blending
  • HDTP


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