Strong completeness for iteration-free coalgebraic dynamic logics

Kupke, Clemens and Hansen, Helle Hvid and Leal, Raul Andres; Diaz, Josep and Lanese, Ivan and Sangiorgi, Davide, eds. (2014) Strong completeness for iteration-free coalgebraic dynamic logics. In: Theoretical Computer Science. Lecture Notes in Computer Science, 8705 . Springer, pp. 281-295. ISBN 978-3-662-44601-0

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    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.

    • Item type:Book Section
      ID code:51156
      Dates:
      Date
      Event
      September 2014
      Published
      20 June 2014
      Accepted
      Notes:The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-662-44602-7_22
      Keywords:propositional dynamic logic, game logic, strong completeness, coalgebraic dynamic modal logic, Mathematics, Computational Theory and Mathematics
      Subjects:Science > Mathematics
      Department:Faculty of Science > Computer and Information Sciences
      Depositing user: Pure Administrator
      Date deposited:19 Jan 2015 12:22
      Last modified:11 Apr 2021 00:57
      Related URLs:
      URI:https://strathprints.strath.ac.uk/id/eprint/51156
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