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Deriving Inverse Operators for Modal Logic

  • Michell Guzmán
  • Salim Perchy
  • Camilo Rueda
  • Frank D. Valencia
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9965)

Abstract

Spatial constraint systems are algebraic structures from concurrent constraint programming to specify spatial and epistemic behavior in multi-agent systems. We shall use spatial constraint systems to give an abstract characterization of the notion of normality in modal logic and to derive right inverse/reverse operators for modal languages. In particular, we shall identify the weakest condition for the existence of right inverses and show that the abstract notion of normality corresponds to the preservation of finite suprema. We shall apply our results to existing modal languages such as the weakest normal modal logic, Hennessy-Milner logic, and linear-time temporal logic. We shall discuss our results in the context of modal concepts such as bisimilarity and inconsistency invariance.

Keywords

Modal logic Inverse operators Constraint systems Modal algebra Bisimulation 

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Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Michell Guzmán
    • 1
  • Salim Perchy
    • 1
  • Camilo Rueda
    • 3
  • Frank D. Valencia
    • 2
    • 3
  1. 1.Inria-LIXÉcole Polytechnique de ParisPalaiseauFrance
  2. 2.CNRS-LIXÉcole Polytechnique de ParisPalaiseauFrance
  3. 3.Pontificia Universidad Javeriana de CaliCaliColombia

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