PP-2001-23: A Modal Walk Through Space

PP-2001-23: Aiello, Marco and van Benthem, Johan (2001) A Modal Walk Through Space. [Report]

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Abstract

We investigate the major mathematical theories of space from a modal standpoint: topology, affine geometry, metric geometry, and vector algebra. This allows us to see new fine-structure in spatial patterns which suggests analogies across these mathematical theories in terms of modal, temporal, and conditional logics. Throughout the modal walk through space, expressive power is analyzed in terms of language design, bisimulations, and correspondence phenomena. The result is both unification across the areas visited, and the uncovering of interesting new questions.

Item Type: Report
Report Nr: PP-2001-23
Series Name: Prepublication (PP) Series
Year: 2001
Uncontrolled Keywords: affine geometry, elementary geometry, betweenness, nearness, mathematical morphology, modal logics of space, spatial reasoning
Subjects: Logic
Date Deposited: 12 Oct 2016 14:36
Last Modified: 12 Oct 2016 14:36
URI: https://eprints.illc.uva.nl/id/eprint/64

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