Modal logic over finite structures

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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DOI 10.1023/A:1008275906015
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Martin Otto (2013). Expressive Completeness Through Logically Tractable Models. Annals of Pure and Applied Logic 164 (12):1418-1453.

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