Abstract
The theory of distributed conceptual structures, as outlined in this paper, is concerned with the distribution and conception of knowledge. It rests upon two related theories, Information Flow and Formal Concept Analysis, which it seeks to unify. Information Flow (IF) [2] is concerned with the distribution of knowledge. The foundations of Information Flow are explicitly based upon the Chu Construction in *- autonomous categories [1] and implicitly based upon the mathematics of closed categories [6]. Formal Concept Analysis (FCA) [3] is concerned with the conception and analysis of knowledge. In this paper, we connect these two studies by categorizing the basic theorem of Formal Concept Analysis, thus extending it to the distributed realm of Information Flow. The main result is the representation of the basic theorem as a categorical equivalence at three different levels of functional and relational constructs. This representation accomplishes a rapprochement between Information Flow and Formal Concept Analysis.
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References
Barr, M.: Autonomous categories and linear logic. Mathematical Structures in Computer Science 1 (1991) 159–178.
Barwise, J., Seligman, J.: Information Flow: the Logic of Distributed Systems. Cambridge University Press, Cambridge (1997).
Ganter, B., Wille, R.: Formal Concept Analysis: Mathematical Foundations. Springer, Heidelberg (1999).
Kent, R.: The Information Flow Foundation for Conceptual Knowledge Organization. Beghtol, C., Howarth, C., Williamson, N. (eds.): Dynamism and Stability in Knowledge Organization. Proceedings of the Sixth International ISKO Conference. Advances in Knowledge Organization 7 (2000) 111–117. Ergon Verlag, Würzburg.
Kent, R.: The IFF Foundation for Ontological Knowledge Organization. Beghtol, C., Williamson, N. (eds.): Knowledge Organization and Classification in International Information Retrieval. Cataloging and Classification Quarterly. The Haworth Press Inc., Binghamton, New York(2003).
Lawvere, W.: Metric Spaces, Generalized Logic and Closed Categories. Rendiconti del Seminario Matematico e Fisico di Milano 43 (1973) 135–166.
Mac Lane, S.: Categories for the Working Mathematician. Springer, New York (1971).
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Kent, R.E. (2002). Distributed Conceptual Structures. In: de Swart, H.C.M. (eds) Relational Methods in Computer Science. RelMiCS 2001. Lecture Notes in Computer Science, vol 2561. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36280-0_8
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DOI: https://doi.org/10.1007/3-540-36280-0_8
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