Strong Completeness for Iteration-Free Coalgebraic Dynamic Logics

  • Helle Hvid Hansen
  • Clemens Kupke
  • Raul Andres Leal
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8705)

Abstract

We present a (co)algebraic treatment of iteration-free dynamic modal logics such as Propositional Dynamic Logic (PDL) and Game Logic (GL), both without star. The main observation is that the program/game constructs of PDL/GL arise from monad structure, and the axioms of these logics correspond to certain compatibilty requirements between the modalities and this monad structure. Our main contribution is a general soundness and strong completeness result for PDL-like logics for T-coalgebras where T is a monad and the ”program” constructs are given by sequential composition, test, and pointwise extensions of operations of T.

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Copyright information

© IFIP International Federation for Information Processing 2014

Authors and Affiliations

  • Helle Hvid Hansen
    • 1
    • 2
  • Clemens Kupke
    • 3
  • Raul Andres Leal
    • 4
  1. 1.Radboud University NijmegenThe Netherlands
  2. 2.CWI AmsterdamThe Netherlands
  3. 3.University of StrathclydeUK
  4. 4.Cap GeminiAmsterdamThe Netherlands

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