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A Hierarchy of Algebras for Boolean Subsets

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Relational and Algebraic Methods in Computer Science (RAMiCS 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12062))

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Abstract

We present a collection of axiom systems for the construction of Boolean subalgebras of larger overall algebras. The subalgebras are defined as the range of a complement-like operation on a semilattice. This technique has been used, for example, with the antidomain operation, dynamic negation and Stone algebras. We present a common ground for these constructions based on a new equational axiomatisation of Boolean algebras. All results are formally proved in Isabelle/HOL.

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Acknowledgement

We thank Andreas Zelend and the anonymous referees for their helpful comments.

Author information

Authors and Affiliations

  1. Department of Computer Science and Software Engineering, University of Canterbury, Christchurch, New Zealand

    Walter Guttmann

  2. Institut für Informatik, Universität Augsburg, Augsburg, Germany

    Bernhard Möller

Authors
  1. Walter Guttmann
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  2. Bernhard Möller
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Corresponding author

Correspondence to Walter Guttmann .

Editor information

Editors and Affiliations

  1. Laboratoire d’informatique (LIX), École Polytechnique, Palaiseau, France

    Uli Fahrenberg

  2. Faculty of Mathematics, Chapman University, Orange, CA, USA

    Peter Jipsen

  3. Department of Computer Science, Brock University, St. Catharines, ON, Canada

    Michael Winter

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Guttmann, W., Möller, B. (2020). A Hierarchy of Algebras for Boolean Subsets. In: Fahrenberg, U., Jipsen, P., Winter, M. (eds) Relational and Algebraic Methods in Computer Science. RAMiCS 2020. Lecture Notes in Computer Science(), vol 12062. Springer, Cham. https://doi.org/10.1007/978-3-030-43520-2_10

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  • DOI: https://doi.org/10.1007/978-3-030-43520-2_10

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-43519-6

  • Online ISBN: 978-3-030-43520-2

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