Euclidean Hierarchy in Modal Logic |
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Authors: | Johan van Benthem Guram Bezhanishvili Mai Gehrke |
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Institution: | (1) Institute for Logic, Language and Computation, University of Amsterdam, Plantage Muidergracht 24, 1018 TV Amsterdam, The Netherlands;(2) Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM 88003-0001, USA |
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Abstract: | 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. |
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Keywords: | Topo-bisimulation serial set chequered set Euclidean hierarchy |
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