A contraction-free and cut-free sequent calculus for propositional dynamic logic

Studia Logica 94 (1):47 - 72 (2010)
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.
Keywords Contraction-free  Cut-free  Propositional Dynamic Logic  Tree-hypersequent  Proof theory
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DOI 10.2307/40587179
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