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Theory blending: extended algorithmic aspects and examples

  • M. Martinez
  • A. M. H. Abdel-Fattah
  • U. Krumnack
  • D. Gómez-Ramírez
  • A. Smaill
  • T. R. Besold
  • A. Pease
  • M. Schmidt
  • M. Guhe
  • K.-U. Kühnberger
Article
  • 152 Downloads

Abstract

In Cognitive Science, conceptual blending has been proposed as an important cognitive mechanism that facilitates the creation of new concepts and ideas by constrained combination of available knowledge. It thereby provides a possible theoretical foundation for modeling high-level cognitive faculties such as the ability to understand, learn, and create new concepts and theories. Quite often the development of new mathematical theories and results is based on the combination of previously independent concepts, potentially even originating from distinct subareas of mathematics. Conceptual blending promises to offer a framework for modeling and re-creating this form of mathematical concept invention with computational means. This paper describes a logic-based framework which allows a formal treatment of theory blending (a subform of the general notion of conceptual blending with high relevance for applications in mathematics), discusses an interactive algorithm for blending within the framework, and provides several illustrating worked examples from mathematics.

Keywords

Concept blending Heuristic-driven theory projection 

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • M. Martinez
    • 1
  • A. M. H. Abdel-Fattah
    • 2
  • U. Krumnack
    • 3
  • D. Gómez-Ramírez
    • 3
  • A. Smaill
    • 4
  • T. R. Besold
    • 5
  • A. Pease
    • 6
  • M. Schmidt
    • 3
  • M. Guhe
    • 4
  • K.-U. Kühnberger
    • 3
  1. 1.Department of MathematicsUniversidad de los AndesBogotáColombia
  2. 2.Faculty of ScienceAin Shams UniversityCairoEgypt
  3. 3.Institute of Cognitive ScienceUniversity of OsnabrückOsnabrückGermany
  4. 4.School of InformaticsUniversity of EdinburghEdinburghUK
  5. 5.The KRDB Research CentreFree University of Bozen-BolzanoBolzanoItaly
  6. 6.School of Science and EngineeringUniversity of DundeeDundeeUK

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