Interpolation for Converse PDL
Johannes Kloibhofer, Valentina Trucco Dalmas, Yde Venema · Lecture notes in computer science · 2025
Abstract Converse $$\textsf{PDL}$$ PDL is the extension of propositional dynamic logic with a converse operation on programs. Our main result states that Converse $$\textsf{PDL}$$ PDL enjoys the (local) Craig Interpolation Property, with respect to both atomic programs and propositional variables. As a corollary we establish the Beth Definability Property for the logic. Our interpolation proof is based on an adaptation of Maehara’s proof-theoretic method. For this purpose we introduce a sound and complete cyclic sequent system for this logic. This calculus features an analytic cut rule and uses a focus mechanism for recognising successful cycles.