A computational account of conceptual blending in basic mathematics

Markus Guhe (Lead / Corresponding author), Alison Pease, Alan Smaill, Maricarmen Martinez, Martin Schmidt, Helmar Gust, Kai-Uwe Kuhnberger, Ulf Krumnack

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    19 Citations (Scopus)

    Abstract

    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
    Volume12
    Issue number3-4
    DOIs
    Publication statusPublished - 2011

    Keywords

    • Conceptual blending
    • Lakoff and Núñez
    • Goguen
    • Mathematical cognition
    • Heuristic-Driven Theory Projection
    • Higher-order anti-unification
    • Analogical inference

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  • Cite this

    Guhe, M., Pease, A., Smaill, A., Martinez, M., Schmidt, M., Gust, H., Kuhnberger, K-U., & Krumnack, U. (2011). A computational account of conceptual blending in basic mathematics. Cognitive Systems Research, 12(3-4), 249-265. https://doi.org/10.1016/j.cogsys.2011.01.004