PP-2002-07:
van Benthem, Johan and Bezhanishvili, Guram and Gehrke, Mai
(2002)
*Euclidean Hierarchy in Modal Logic.*
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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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