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The Logic of Discrete Qualitative Relations

Authors Giulia Sindoni, John G. Stell

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Giulia Sindoni
John G. Stell

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Giulia Sindoni and John G. Stell. The Logic of Discrete Qualitative Relations. In 13th International Conference on Spatial Information Theory (COSIT 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 86, pp. 1:1-1:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017) https://doi.org/10.4230/LIPIcs.COSIT.2017.1

Abstract

We consider a modal logic based on mathematical morphology which allows the expression of mereotopological relations between subgraphs in the setting of the discrete space. A specific form of topological closure for graphs can be expressed in the logic, as a combination of the negation and its bi-intuitionistic dual, as well as a modality, using the stable relation Q, which describes the incidence structure of the graph. By working in this context we have been able to define qualitative spatial relations between discrete regions, and to compare them with earlier works in mereotopology, both in the discrete and in the continuous space.

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Keywords
  • modal logic
  • qualitative spatial reasoning
  • discrete space

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