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Towards a Mathematical Theory of Knowledge^*

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Abstract

A typed category theory is proposed for the abstract description of knowledge and knowledge processing. It differs from the traditional category theory in two directions: all morphisms have types and the composition of morphisms is not necessary a morphism. Two aspects of application of typed category theory are discussed: cones and limits of knowledge complexity classes and knowledge completion with pseudo-functors.

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Authors and Affiliations

  1. Key Lab of IIPL, Institute of Computing Technology, Chinese Academy of Sciences, Beijing, 100080, P.R. China

    Ru-Qian Lu

  2. Key Lab of MADIS, Chinese Academy of Sciences, Beijing, 100080, P.R. China

    Ru-Qian Lu

  3. Institute of Mathematics, AMSS, Chinese Academy of Sciences, Beijing, 100080, P.R. China

    Ru-Qian Lu

  4. Shanghai Key Lab of IIPL, Fudan University, Shanghai, 200433, P.R. China

    Ru-Qian Lu

  5. Beijing Key Lab of ISMM, Beijing University of Technology, Beijing, 100022, P.R. China

    Ru-Qian Lu

Authors
  1. Ru-Qian Lu
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Correspondence to Ru-Qian Lu.

Additional information

Supported by the National Basic Research 973 Program of China under Grant Nos. 2001CCA03000, 2001AA113130, 2001CB312004 and the Major Program of the National Natural Science Foundation of China under Grant No.

A preliminary version of this paper appeared in Proc. KEST 2004, Beijing

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Lu, RQ. Towards a Mathematical Theory of Knowledge^*. J Comput Sci Technol 20, 751–757 (2005). https://doi.org/10.1007/s11390-005-0751-4

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  • DOI: https://doi.org/10.1007/s11390-005-0751-4

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