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International Joint Conference on Automated Reasoning

IJCAR 2014: Automated Reasoning pp 307–321Cite as

Axioms vs Hypersequent Rules with Context Restrictions: Theory and Applications

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8562))

Abstract

We introduce transformations between hypersequent rules with context restrictions and Hilbert axioms extending classical (and intuitionistic) propositional logic and vice versa. The introduced rules are used to prove uniform cut elimination, decidability and complexity results as well as finite axiomatisations for many modal logics given by simple frame properties. Our work subsumes many logic-tailored results and allows for new results. As a case study we apply our methods to the logic of uniform deontic frames.

Supported by FWF START Y544-N23.

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Author information

Authors and Affiliations

  1. TU Vienna, Vienna, Austria

    Björn Lellmann

Authors
  1. Björn Lellmann
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Editor information

Editors and Affiliations

  1. CNRS,, New York University &amp, USA

    Stéphane Demri

  2. Department of Computer Science, University of New Mexico, 87131-0001, Albuquerque, NM, USA

    Deepak Kapur

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

    Christoph Weidenbach

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© 2014 Springer International Publishing Switzerland

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Lellmann, B. (2014). Axioms vs Hypersequent Rules with Context Restrictions: Theory and Applications. In: Demri, S., Kapur, D., Weidenbach, C. (eds) Automated Reasoning. IJCAR 2014. Lecture Notes in Computer Science(), vol 8562. Springer, Cham. https://doi.org/10.1007/978-3-319-08587-6_23

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  • DOI: https://doi.org/10.1007/978-3-319-08587-6_23

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08586-9

  • Online ISBN: 978-3-319-08587-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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