Euclidean hierarchy in modal logic

Studia Logica 75 (3):327-344 (2003)
For a Euclidean space , let L n denote the modal logic of chequered subsets of . For every n 1, we characterize L n using the more familiar Kripke semantics, thus implying that each L n is a tabular logic over the well-known modal system Grz of Grzegorczyk. We show that the logics L n form a decreasing chain converging to the logic L of chequered subsets of . As a result, we obtain that L is also a logic over Grz, and that L has the finite model property. We conclude the paper by extending our results to the modal language enriched with the universal modality.
Keywords Philosophy   Logic   Mathematical Logic and Foundations   Computational Linguistics
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DOI 10.1023/B:STUD.0000009564.00287.16
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Marco Aiello & Johan van Benthem (2002). A ModalWalk Through Space. Journal of Applied Non-Classical Logics 12 (3-4):319-363.

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