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Nominal Renaming Sets

  • Conference paper
Logic for Programming, Artificial Intelligence, and Reasoning (LPAR 2008)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5330))

Abstract

Nominal techniques are based on the idea of sets with a finitely-supported atoms-permutation action.

We consider the idea of nominal renaming sets, which are sets with a finitely-supported atoms-renaming action; renamings can identify atoms, permutations cannot. We show that nominal renaming sets exhibit many of the useful qualities found in (permutative) nominal sets; an elementary sets-based presentation, inductive datatypes of syntax up to binding, cartesian closure, and being a topos. Unlike is the case for nominal sets, the notion of names-abstraction coincides with functional abstraction. Thus we obtain a concrete presentation of sheaves on the category of finite sets in the form of a category of sets with structure.

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Author information

Authors and Affiliations

  1. UK

    Murdoch J. Gabbay

  2. Germany

    Martin Hofmann

Authors
  1. Murdoch J. Gabbay
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  2. Martin Hofmann
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Editor information

Editors and Affiliations

  1. Carnegie Mellon University, Doha, Qatar

    Iliano Cervesato

  2. Technische Universität Darmstadt, Germany

    Helmut Veith

  3. University of Manchester, UK

    Andrei Voronkov

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Gabbay, M.J., Hofmann, M. (2008). Nominal Renaming Sets. In: Cervesato, I., Veith, H., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2008. Lecture Notes in Computer Science(), vol 5330. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89439-1_11

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  • DOI: https://doi.org/10.1007/978-3-540-89439-1_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-89438-4

  • Online ISBN: 978-3-540-89439-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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