Modal logics of reactive frames

Dov M. Gabbay, Sérgio Marcelino

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


A reactive graph generalizes the concept of a graph by making it dynamic, in the sense that the arrows coming out from a point depend on how we got there. This idea was first applied to Kripke semantics of modal logic in [2]. In this paper we strengthen that unimodal language by adding a second operator. One operator corresponds to the dynamics relation and the other one relates paths with the same endpoint. We explore the expressivity of this interpretation by axiomatizing some natural subclasses of reactive frames. The main objective of this paper is to present a methodology to study reactive logics using the existent classic techniques.

Original languageEnglish
Pages (from-to)405-446
Number of pages42
JournalStudia Logica
Issue number2
StatePublished - Dec 2009

Bibliographical note

Funding Information:
Acknowledgements. This work was partially supported by FCT and EU FEDER, via the KLog project PTDC/MAT/68723/2006 of SQIG-IT and by FCT PhD fellowship SFRH/BD/27938/2006.


  • (bi)modal logic
  • Kripke semantics
  • Reactive frames
  • Reactive graphs


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