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arXiv · 2508.21485

Interpolation for Converse PDL

Johannes Kloibhofer·Valentina Trucco Dalmas·Yde Venema
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Abstract

Converse PDL is the extension of propositional dynamic logic with a converse operation on programs. Our main result states that Converse 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.

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Johannes Kloibhofer, Valentina Trucco Dalmas, Yde Venema. 2025-08-29. Interpolation for Converse PDL. https://arxiv.org/abs/2508.21485

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