Studia Logica

, Volume 94, Issue 1, pp 47–72 | Cite as

A Contraction-free and Cut-free Sequent Calculus for Propositional Dynamic Logic

  • Brian Hill
  • Francesca Poggiolesi


In this paper we present a sequent calculus for propositional dynamic logic built using an enriched version of the tree-hypersequent method and including an infinitary rule for the iteration operator. We prove that this sequent calculus is theoremwise equivalent to the corresponding Hilbert-style system, and that it is contraction-free and cut-free. All results are proved in a purely syntactic way.


Contraction-free Cut-free Propositional Dynamic Logic Tree-hypersequent Proof theory 


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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Center of Logic and Philosophy of Science (CLFW)Vrije Universiteit BrusselBrusselsBelgium
  2. 2.HEC Paris and IHPST (CNRS / Paris 1 / ENS)Jouy-en-JosasFrance

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