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Conference Papers Year : 2014

Strong Completeness for Iteration-Free Coalgebraic Dynamic Logics

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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hal-01402072 , version 1 (24-11-2016)

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Helle Hvid Hansen, Clemens Kupke, Raul Andres Leal. Strong Completeness for Iteration-Free Coalgebraic Dynamic Logics. 8th IFIP International Conference on Theoretical Computer Science (TCS), Sep 2014, Rome, Italy. pp.281-295, ⟨10.1007/978-3-662-44602-7_22⟩. ⟨hal-01402072⟩
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