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Modular Construction of Modal Logics

Corina Cirstea and Dirk Pattinson

Presented at Fifteenth International Conference on Concurrency Theory (CONCUR 2004), London, England, 31 August - 3 September, 2004


We present a modular approach to defining logics for a wide variety of state-based systems. We use coalgebras to model the behaviour of systems, and modal logics to specify behavioural properties of systems. We show that the syntax, semantics and proof systems associated to such logics can all be derived in a modular way. Moreover, we show that the logics thus obtained inherit soundness, completeness and expressiveness properties from their building blocks. We apply these techniques to derive sound, complete and expressive logics for a wide variety of probabilistic systems.

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