A Non-wellfounded, Labelled Proof System for Propositional Dynamic Logic
Abstract
We define a infinitary labelled sequent calculus for PDL, G3PDL∞. A finitarily representable cyclic system, G3PDLω, is then given. We show that both are sound and complete with respect to standard models of PDL and, further, that G3PDL∞ is cut-free complete. We additionally investigate proof-search strategies in the cyclic system for the fragment of PDL without tests.
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