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Introduction to the Mathematical Theory of Knowledge Conceptualization: Conceptual Systems and Structures

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Applied Informatics (ICAI 2019)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1051))

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Abstract

The paper departs from the general problem of knowledge integration and the basic strategies that can be adopted to confront this challenge. With the purpose of providing a sound meta-theoretical framework to facilitate knowledge conceptualization and integration, as well as assessment criteria to evaluate achievements regarding knowledge integration, the paper first reviews the previous work in the field of conceptual spaces. It subsequently gives an overview of structural tools and mechanisms for knowledge representation, recapped in the modal stratified bond model of global knowledge. On these groundings, a novel formalized representation of conceptual systems, structures, spaces and algebras is developed through a set of definitions which goes beyond the exploration of mental knowledge representation and the semantics of natural languages. These two components provide a sound framework for the development of the glossaLAB international project with respect to its two basic objectives, namely (i) facilitating knowledge integration in general and particularly in the context of the general study of information and systems; (ii) facilitating the assessment of the achievements as regards knowledge integration in interdisciplinary settings. An additional article tackles the solutions adopted to integrate these results in the elucidation of the conceptual network of the general study of information and systems.

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References

  1. Adams, B., Raubal, M.: A metric conceptual space algebra. In: Hornsby, K.S., Claramunt, C., Denis, M., Ligozat, G. (eds.) COSIT 2009. LNCS, vol. 5756, pp. 51–68. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-03832-7_4

    Chapter  Google Scholar 

  2. Aerts, D., Gabora, L.: A state-context-property model of concepts and their combinations II: a Hilbert space representation. Kybernetes 34(1/2), 176–204 (2005)

    MATH  Google Scholar 

  3. Albert, D., Lukas, J. (eds.): Knowledge Spaces: Theories, Empirical Research. Applications. Lawrence Erlbaum Associates, Mahwah (1999)

    Google Scholar 

  4. Balzer, W., Moulines, C.U., Sneed, J.D.: An Architectonic for Science: The Structuralist Program. Reidel, Dordrecht (1987)

    Book  Google Scholar 

  5. Barabási, A.-L.: Linked: The New Science of Networks. Perseus, Cambridge (2002)

    Google Scholar 

  6. Barrett, E. (ed.): Text, Context and Hypertext: Writing with and for the Computer. MIT Press, Cambridge (1988)

    Google Scholar 

  7. Bolt, J., Coecke, B., Genovese, F., Lewis, M., Marsden, D., Piedeleu, R.: Interacting conceptual spaces: grammatical composition of concepts. In: Kaipainen, M., Zenker, F., Hautamäki, A., Gärdenfors, P. (eds.) Conceptual Spaces: Elaborations and Applications, pp. 11–19. Springer, Cham (2017). https://doi.org/10.1007/978-3-030-12800-5_9

    Chapter  Google Scholar 

  8. Burgin, M., de Vey Mestdagh, C.N.J.: Consistent structuring of inconsistent knowledge. J. Intell. Inf. Syst. 45(1), 5–28 (2015)

    Article  Google Scholar 

  9. Burgin, M., Gladun, V.: Mathematical foundations of semantic networks theory. In: Demetrovics, J., Thalheim, B. (eds.) MFDBS 1989. LNCS, vol. 364, pp. 117–135. Springer, Heidelberg (1989). https://doi.org/10.1007/3-540-51251-9_9

    Chapter  Google Scholar 

  10. Burgin, M., Gorsky, D.P.: Towards the construction of a general theory of concept. In: The Opened Curtain, pp. 167–195. Oulder, San Francisco, Oxford (1991)

    Google Scholar 

  11. Burgin, M., Kuznetsov, V.: Introduction to Modern Exact Methodology of Science. International Science Foundation, Moscow (1994). (in Russian)

    Google Scholar 

  12. Burgin, M.: Logical varieties and covarieties. In: Methodological and Theoretical Problems of Mathematics and Information and Computer Sciences, Kiev, pp. 18–34 (1997). (in Russian)

    Google Scholar 

  13. Burgin, M.: Named sets as a basic tool in epistemology. Epistemologia, XVIII, 87–110 (1995)

    Google Scholar 

  14. Burgin, M.: Named sets in the semantic network theory. In: Knowledge - Dialog - Decision, pp. 43–47. Leningrad (1991). (in Russian)

    Google Scholar 

  15. Burgin, M.: Structural Reality. Nova Science Publishers, New York (2012)

    MATH  Google Scholar 

  16. Burgin, M.: Theory of Information: Fundamentality, Diversity and Unification. World Scientific Publishing, Singapore (2010)

    MATH  Google Scholar 

  17. Burgin, M.: Theory of Knowledge: Structures and Processes. World Scientific, New York/London/Singapore (2017)

    MATH  Google Scholar 

  18. Burgin, M.: Theory of Named Sets. Mathematics Research Developments. Nova Science, New York (2011)

    MATH  Google Scholar 

  19. Burgin, M.: Weighted e-spaces and epistemic information operators. Information 5(3), 357–388 (2014)

    Article  Google Scholar 

  20. Carnap, R.: The Logical Syntax of Language. Humanities, New York (1937)

    MATH  Google Scholar 

  21. Cohen, B., Murphy, G.L.: Models of concepts. Cogn. Sci. 8(1), 27–58 (1984)

    Article  Google Scholar 

  22. Díaz-Nafría, J.M., Burgin, M., Rodriguez-Bravo, B.: Knowledge structures and conceptual networks for evaluation of knowledge integration. In: Dodig-Crnkovic, G., Burgin, M. (eds.) Philosophy and Methodology of Information: The Study of Information in the Transdisciplinary Perspective, pp. 457–489. World Scientific, Singapore (2019)

    Chapter  Google Scholar 

  23. Díaz-Nafría, J.M., Guarda, T., Coronel, I.: A network theoretical approach to assess knowledge integration in information studies. In: Rocha, Á., Guarda, T. (eds.) Smart Innovation, Systems and Technologies, vol. 94, pp. 360–371. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-78605-6_31

    Chapter  Google Scholar 

  24. Díaz-Nafría, J.M., et al.: glossaLAB: Co-creating Interdisciplinary Knowledge. In: Proceedings of the Second International Conference on Applied Informatics. Communications in Computer and Information Science (2019). [In Press]

    Google Scholar 

  25. Díaz-Nafría, J.M.: Cyber-subsidiarity: toward a global sustainable information society. In: Carayannis, E.G., et al. (eds.) Handbook of Cyber-Development, Cyber-Democracy, and Cyber-Defense, pp. 1–30. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-09069-6_39

    Chapter  Google Scholar 

  26. Doignon, J.-P., Falmagne, J.-Cl.: Knowledge Spaces. Springer, Heidelberg (1999). https://doi.org/10.1007/978-3-642-58625-5

    Book  MATH  Google Scholar 

  27. Fauconnier, G., Turner, M.: The Way We Think: Conceptual Blending and the Mind’s Hidden Complexities. Basic Books, New York (2002)

    Google Scholar 

  28. Frege, G.: Über Sinn und Bedeutung. Zeitschrift für Philosophie und philosophische Kritik 100, 25–50 (1892)

    Google Scholar 

  29. Gärdenfors, P., Löhndorf, S.: What is a domain? Dimensional structures vs- meronymic relations. Cogn. Linguist. 24, 437–456 (2013)

    Article  Google Scholar 

  30. Gärdenfors, P.: Cognitive semantics and image schemas with embodied forces. In: Krois, J.M., Rosengren, M., Steidele, A., Westerkamp, D. (eds.) Embodiment in cognition and culture, pp. 57–76. Benjamins, Amsterdam (2007)

    Chapter  Google Scholar 

  31. Gärdenfors, P.: Conceptual spaces as a framework for knowledge representation. Mind Matter 2(2), 9–27 (2004)

    Google Scholar 

  32. Gärdenfors, P.: Conceptual Spaces: On the Geometry of Thought. MIT Press, Cambridge (2000)

    Book  Google Scholar 

  33. Gärdenfors, P.: Geometry of Meaning: Semantics Based on Conceptual Spaces. MIT Press, Cambridge (2014)

    Book  Google Scholar 

  34. Gärdenfors, P.: Semantic Knowledge, Domains of Meaning and Conceptual Spaces. In: Meusburger, P., Werlen, B., Suarsana, L. (eds.) Knowledge and Action. Knowledge and Space, vol. 9. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-44588-5_12

    Chapter  Google Scholar 

  35. Garrison, J.W.: Hintikka, Laudan and Newton: an interrogative model of scientific discovery. Synthese 74(2), 45–172 (1988)

    Article  MathSciNet  Google Scholar 

  36. Hampton, J.A.: Concepts and natural language. In: Concepts and Fuzzy Logic, pp. 233–258, MIT Press, Cambridge (2011)

    Google Scholar 

  37. Hempel, C.G.: Fundamentals of concept formation in empirical science. In: International Encyclopedia of Unified Science, vol. 2, no. 7. University of Chicago Press, Chicago (1952)

    Google Scholar 

  38. Jago, M.: Logical information and epistemic space. Synthese 167(2), 327–341 (2009)

    Article  MathSciNet  Google Scholar 

  39. Kuhn, T.: The Structure of Scientific Revolutions. The University of Chicago Press, Chicago (1970)

    Google Scholar 

  40. Lakatos, I.: The Methodology of Scientific Research Programmes. Cambridge University Press, Cambridge (1978)

    Book  Google Scholar 

  41. Lewis, M., Lawry, J.: Hierarchical conceptual spaces for concept combination. Artif. Intell. 237, 204–227 (2016)

    Article  MathSciNet  Google Scholar 

  42. Losee, J.: A Historical Introduction to the Philosophy of Science. Oxford University Press, New York (2001)

    MATH  Google Scholar 

  43. Muyeba, M., Rybakov, V.: Knowledge Representation in Agent’s Logic with Uncertainty and Agent’s Interaction, Preprint in Computer Science, 1406.5495 [cs.LO] (2014). Electronic edition in: http://arXiv.org. Accessed 10 Aug 2019

  44. Nielsen, J.: Hypertext and Hypermedia. Academic Press, New York (1990)

    Google Scholar 

  45. Osgood, C.E., Suci, G.J., Tannenbaum, P.H.: The Measurement of Meaning. University of Illinois Press, Urbana (1978)

    Google Scholar 

  46. Popper, K.R.: Objective Knowledge: An Evolutionary Approach. Oxford University Press, New York (1979)

    Google Scholar 

  47. Rao, V.S.: Theories of knowledge: Its Validity and its Sources. Sri Satguru Publications, Delhi (1998)

    Google Scholar 

  48. Rickard, J., Aisbett, J., Gibbon, G.: Reformulation of the theory of conceptual spaces. Inf. Sci. 177(21), 4539–4565 (2007)

    Article  MathSciNet  Google Scholar 

  49. Russell, B.: On denoting. Mind 14, 479–493 (1905)

    Article  Google Scholar 

  50. Sowa, J.F.: Semantic networks. In: Encyclopedia of Artificial Intelligence. Wiley, New York (1987)

    Google Scholar 

  51. Suppe, F.: The Positivist Model of Scientific Theories, in Scientific Inquiry. Oxford University Press, New York (1999)

    Google Scholar 

  52. Suppes, P.: What is a scientific theory? In: Philosophy of Science Today, pp. 55–67. Basic Books, New York (1967)

    Google Scholar 

  53. Thagard, P.: Computational Philosophy of Science. A Bradford Book, Oxford (1988)

    Book  Google Scholar 

  54. van Frassen, B.: The semantic approach to scientific theories. In: Sklar, L. (ed.) The Nature of Scientific Theory, pp. 175–194. Garland, New York (2000)

    Google Scholar 

  55. Zhuge, H.: The Knowledge Grid: Toward Cyber-Physical Society. World Scientific Publishing, Singapore (2012)

    Book  Google Scholar 

  56. Zimmermann, R.E.: New Ethics Proved in Geometrical Order. Spinozist Reflections on Evolutionary Systems. Emergent Publications, Litchfield Parz (2010)

    Google Scholar 

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Acknowledgment

This contribution has been carried out under support of glossaLAB project, co-founded by the Universidad Estatal Península de Santa Elena, Ecuador, and an international consortium of academic institutions. The authors wish to dedicate this work to the memory of Charles François whose work represents an invaluable and everlasting contribution to the integration of knowledge.

Author information

Authors and Affiliations

  1. University of California, Los Angeles, CA, USA

    Mark Burgin

  2. Madrid Open University, Madrid, Spain

    José María Díaz-Nafría

Authors
  1. Mark Burgin
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  2. José María Díaz-Nafría
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Corresponding author

Correspondence to José María Díaz-Nafría .

Editor information

Editors and Affiliations

  1. Universidad Distrital Francisco Jose de Caldas, Bogota, Colombia

    Hector Florez

  2. Universidad Nacional de Loja, Loja, Ecuador

    Marcelo Leon

  3. Universidad a Distancia de Madrid, Madrid, Spain

    Jose Maria Diaz-Nafria

  4. Universidad Complutense de Madrid, Madrid, Spain

    Simone Belli

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Burgin, M., Díaz-Nafría, J.M. (2019). Introduction to the Mathematical Theory of Knowledge Conceptualization: Conceptual Systems and Structures. In: Florez, H., Leon, M., Diaz-Nafria, J., Belli, S. (eds) Applied Informatics. ICAI 2019. Communications in Computer and Information Science, vol 1051. Springer, Cham. https://doi.org/10.1007/978-3-030-32475-9_34

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  • DOI: https://doi.org/10.1007/978-3-030-32475-9_34

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-32474-2

  • Online ISBN: 978-3-030-32475-9

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