Constructing Cut Free Sequent Systems with Context Restrictions Based on Classical or Intuitionistic Logic

  • Björn Lellmann
  • Dirk Pattinson
Conference paper

DOI: 10.1007/978-3-642-36039-8_14

Part of the Lecture Notes in Computer Science book series (LNCS, volume 7750)
Cite this paper as:
Lellmann B., Pattinson D. (2013) Constructing Cut Free Sequent Systems with Context Restrictions Based on Classical or Intuitionistic Logic. In: Lodaya K. (eds) Logic and Its Applications. ICLA 2013. Lecture Notes in Computer Science, vol 7750. Springer, Berlin, Heidelberg

Abstract

We consider a general format for sequent rules for not necessarily normal modal logics based on classical or intuitionistic propositional logic and provide relatively simple local conditions ensuring cut elimination for such rule sets. The rule format encompasses e.g. rules for the boolean connectives and transitive modal logics such as S4 or its constructive version. We also adapt the method of constructing suitable rule sets by saturation to the intuitionistic setting and provide a criterium for translating axioms for intuitionistic modal logics into sequent rules. Examples include constructive modal logics and conditional logic \(\mathbb{VA}\).

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Björn Lellmann
    • 1
  • Dirk Pattinson
    • 2
  1. 1.Department of ComputingImperial College LondonUK
  2. 2.Research School of Computer ScienceThe Australian National UniversityAustralia

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