Abstract : 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.
https://hal-hec.archives-ouvertes.fr/hal-00521802 Contributor : Antoine HaldemannConnect in order to contact the contributor Submitted on : Tuesday, September 28, 2010 - 3:31:39 PM Last modification on : Tuesday, October 19, 2021 - 11:00:09 AM
Brian Hill, Francesca Poggiolesi. A Contraction-free and Cut-free Sequent Calculus for Propositional Dynamic Logic. Studia Logica, Springer Verlag (Germany), 2010, 94 (1), pp.47-72. ⟨10.1007/s11225-010-9224-z⟩. ⟨hal-00521802⟩