We investigate properties of propositional modal logic over the classof finite structures. In particular, we show that certain knownpreservation theorems remain true over this class. We prove that aclass of finite models is defined by a first-order sentence and closedunder bisimulations if and only if it is definable by a modal formula.We also prove that a class of finite models defined by a modal formulais closed under extensions if and only if it is defined by a -modal formula.
Keywords modal logic  finite model theory  preservation theorems
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Reprint years 2004
DOI 10.1023/A:1008275906015
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Modal Characterisation Theorems Over Special Classes of Frames.Anuj Dawar & Martin Otto - 2009 - Annals of Pure and Applied Logic 161 (1):1-42.
Modal and Guarded Characterisation Theorems Over Finite Transition Systems.Martin Otto - 2004 - Annals of Pure and Applied Logic 130 (1-3):173-205.
Expressive Completeness Through Logically Tractable Models.Martin Otto - 2013 - Annals of Pure and Applied Logic 164 (12):1418-1453.

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