ML-1995-08: Modal Logic over Finite Structures

ML-1995-08: Rosen, Eric (1995) Modal Logic over Finite Structures. [Report]

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In this paper, we develop various aspects of the finite model theory of propositional modal logic. In particular, we show that certain results about the expressive power of modal logic over the class of all structures, due to van Benthem and his collaborators, remain true over the class of finite structures. We establish that a first-order definable class of finite models is closed under bisimulations iff it is definable by a `modal first-order sentence'. We show that a class of finite models that is defined by a modal sentence is closed under extensions iff it is defined by a diamond-modal sentence. In sharp contrast, it is well known that many classical results for first-order logic, including various preservation theorems, fail for the class of finite models.

Item Type: Report
Report Nr: ML-1995-08
Series Name: Mathematical Logic and Foundations (ML)
Year: 1995
Date Deposited: 12 Oct 2016 14:40
Last Modified: 12 Oct 2016 14:40

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