We see cut-free sequent systems for the basic normal modal logics formed by any combination the axioms d, t, b, 4, 5. These systems are modular in the sense that each axiom has a corresponding rule and each combination of these rules is complete for the corresponding frame conditions. The systems are based on nested sequents, a natural generalisation of hypersequents. Nested sequents stay inside the modal language, as opposed to both the display calculus and labelled sequents. The completeness proof is via syntactic cut elimination.


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© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Kai Brünnler
    • 1
  • Lutz Straßburger
    • 2
  1. 1.Institut für angewandte Mathematik und InformatikBernSwitzerland
  2. 2.École Polytechnique, Laboratoire d’Informatique (LIX), Projet ParsifalPalaiseau CedexFrance

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