Studia Logica

, Volume 100, Issue 1–2, pp 385–397 | Cite as

Dynamic Modalities



A new modal logic containing four dynamic modalities with the following informal reading is introduced: \({\square^\forall}\)always necessary, \({\square^\exists}\)sometimes necessary, and their duals – \({\diamondsuit^\forall}\)always possibly, and \({\diamondsuit^\exists}\)sometimes possibly. We present a complete axiomatization with respect to the intended formal semantics and prove decidability via fmp.


modal logic dynamic modalities completeness theorem canonical construction filtration 


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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Faculty of Mathematics and InformaticsSofiaBulgaria

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