A Non-wellfounded, Labelled Proof System for Propositional Dynamic Logic

摘要

We define an infinitary labelled sequent calculus for PDL, G3PDL~∞. A finitarily representable cyclic system, G3PDL~ω, 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.