Algorithmic problems concerning first-order definability of modal formulas on the class of all finite frames

Studia Logica 55 (3):421 - 448 (1995)
The main result is that is no effective algorithmic answer to the question:how to recognize whether arbitrary modal formula has a first-order equivalent on the class of finite frames. Besides, two known problems are solved: it is proved algorithmic undecidability of finite frame consequence between modal formulas; the difference between global and local variants of first-order definability of modal formulas on the class of transitive frames is shown.
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DOI 10.1007/BF01057806
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Johan van Benthem (1989). Logical Constants Across Varying Types. Notre Dame Journal of Formal Logic 30 (3):315-342.

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