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A Mechanised Abstract Formalisation of Concept Lattices

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Relational and Algebraic Methods in Computer Science (RAMICS 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8428))

Abstract

Using the dependently-typed programming language Agda, we formalise a category of algebraic contexts with relational homomorphisms presented by [Jip12], [Mos13]. We do this in the abstract setting of locally ordered categories with converse (OCCs) with residuals and direct powers, without requiring meets (as in allegories) or joins (as in Kleene categories). The abstract formalisation has the advantage that it can be used both for theoretical reasoning, and for executable implementations, by instantiating it with appropriate choices of concrete OCCs.

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Author information

Authors and Affiliations

  1. McMaster University, Hamilton, Ontario, Canada

    Wolfram Kahl

Authors
  1. Wolfram Kahl
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Editor information

Editors and Affiliations

  1. NICTA and UNSW, Anzac Parade 223, 2033, Kensington, NSW, Australia

    Peter Höfner

  2. School of Computational Sciences, Chapman University, One University Drive, 92866, Orange, CA, USA

    Peter Jipsen

  3. Department of Computing and Software, McMaster University, 1280 Main Street West, L8S 4K1, Hamilton, ON, Canada

    Wolfram Kahl

  4. Department of Computer Science, University of Augsburg, Universitätsstraße 6a, 86159, Augsburg, Germany

    Martin Eric Müller

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Kahl, W. (2014). A Mechanised Abstract Formalisation of Concept Lattices. In: Höfner, P., Jipsen, P., Kahl, W., Müller, M.E. (eds) Relational and Algebraic Methods in Computer Science. RAMICS 2014. Lecture Notes in Computer Science, vol 8428. Springer, Cham. https://doi.org/10.1007/978-3-319-06251-8_15

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  • DOI: https://doi.org/10.1007/978-3-319-06251-8_15

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-06250-1

  • Online ISBN: 978-3-319-06251-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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