PSPACE-completeness of bimodal transitive weak-density logic

Philippe Balbiani; Olivier Gasquet

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arXiv · 2507.14949

PSPACE-completeness of bimodal transitive weak-density logic

Philippe Balbiani·Olivier Gasquet

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Abstract

Windows have been introduce in \cite{BalGasq25} as a tool for designing polynomial algorithms to check satisfiability of a bimodal logic of weak-density. In this paper, after revisiting the ``folklore'' case of bimodal $\K4$ already treated in \cite{Halpern} but which is worth a fresh review, we show that windows allow to polynomially solve the satisfiability problem when adding transitivity to weak-density, by mixing algorithms for bimodal K together with windows-approach. The conclusion is that both satisfiability and validity are PSPACE-complete for these logics.

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Philippe Balbiani, Olivier Gasquet. 2025-07-20. PSPACE-completeness of bimodal transitive weak-density logic. https://arxiv.org/abs/2507.14949

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