Dynamic Modalities

  • Authors:
  • Dimiter Vakarelov

  • Affiliations:
  • Faculty of Mathematics and Informatics, Sofia, Bulgaria

  • Venue:
  • Studia Logica
  • Year:
  • 2012

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Abstract

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.