PP-2002-07: van Benthem, Johan and Bezhanishvili, Guram and Gehrke, Mai (2002) Euclidean Hierarchy in Modal Logic. [Report]
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Abstract
For an Euclidean space $\mathbb{R}^n$, let $L_n$ denote the modal
logic of chequered subsets of $\mathbb{R}^n$. For every $n\geq 1$, 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 $L_\infty$ of chequered
subsets of $\mathbb{R}^\infty$. As a result, we obtain that $L_\infty$
is also a logic over Grz, and that $L_\infty$ has the finite model
property.
| Item Type: | Report |
|---|---|
| Report Nr: | PP-2002-07 |
| Series Name: | Prepublication (PP) Series |
| Year: | 2002 |
| Uncontrolled Keywords: | Topo-bisimulation, serial set, chequered set, Euclidean hierarchy. |
| Date Deposited: | 12 Oct 2016 14:36 |
| Last Modified: | 12 Oct 2016 14:36 |
| URI: | https://eprints.illc.uva.nl/id/eprint/71 |
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