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Canonical Calculi: Invertibility, Axiom Expansion and (Non)-determinism

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Computer Science - Theory and Applications (CSR 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5675))

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Abstract

We apply the semantic tool of non-deterministic matrices to characterize two important properties of canonical Gentzen-type calculi: invertibility of rules and axiom expansion. We show that in every canonical calculus G satisfying a natural condition, the following are equivalent: (i) the connectives of G admit axiom expansion, (ii) the rules of G are invertible, and (iii) G has a characteristic finite deterministic matrix.

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Author information

Authors and Affiliations

  1. Tel-Aviv University, Israel

    Arnon Avron & Anna Zamansky

  2. Vienna University of Technology, Austria

    Agata Ciabattoni

Authors
  1. Arnon Avron
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  2. Agata Ciabattoni
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  3. Anna Zamansky
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Editor information

Editors and Affiliations

  1. Sobolev Institute of Mathematics SB RAS, 4 Koptyug av, 630090, Novosibirsk, Russia

    Anna Frid

  2. Sobolev Institute of Mathematics SB RAS, Koptyug av. 4, 630090, Novosibirsk, Russia

    Andrey Morozov

  3. Max Planck Institute for Software Systems, Campus E1 4, 66123, Saarbrücken, Germany

    Andrey Rybalchenko

  4. Lehrstuhl für Theoretische Informatik, Institut für Informatik, Julius-Maximilians-Universität Würzburg, Am Hubland, 97974, Würzburg, Germany

    Klaus W. Wagner

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© 2009 Springer-Verlag Berlin Heidelberg

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Avron, A., Ciabattoni, A., Zamansky, A. (2009). Canonical Calculi: Invertibility, Axiom Expansion and (Non)-determinism. In: Frid, A., Morozov, A., Rybalchenko, A., Wagner, K.W. (eds) Computer Science - Theory and Applications. CSR 2009. Lecture Notes in Computer Science, vol 5675. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03351-3_5

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  • DOI: https://doi.org/10.1007/978-3-642-03351-3_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03350-6

  • Online ISBN: 978-3-642-03351-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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