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DOI: 10.4230/LIPIcs.COSIT.2024.17

A Logic of East and West for Intervals (Short Paper)

Authors: Zekai Li, Amin Farjudian, and Heshan Du

Published in: LIPIcs, Volume 315, 16th International Conference on Spatial Information Theory (COSIT 2024)

Abstract

This paper proposes a logic of east and west for intervals (LEWI), which extends the logic of east and west for points. For intervals in 1D Euclidean space, the logic LEWI formalises the qualitative direction relations "east", "west", "definitely east", "definitely west", "partially east", "partially west", etc. To cope with imprecision in geometry representations, the logic LEWI is parameterized by a margin of error σ ∈ ℝ_{> 0} and a level of indeterminacy in directions τ ∈ ℕ_{> 1}. For every τ, we provide an axiomatisation of the logic LEWI, and prove that it is sound and complete with respect to 1D Euclidean space.

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Zekai Li, Amin Farjudian, and Heshan Du. A Logic of East and West for Intervals (Short Paper). In 16th International Conference on Spatial Information Theory (COSIT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 315, pp. 17:1-17:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{li_et_al:LIPIcs.COSIT.2024.17,
  author =	{Li, Zekai and Farjudian, Amin and Du, Heshan},
  title =	{{A Logic of East and West for Intervals}},
  booktitle =	{16th International Conference on Spatial Information Theory (COSIT 2024)},
  pages =	{17:1--17:8},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-330-0},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{315},
  editor =	{Adams, Benjamin and Griffin, Amy L. and Scheider, Simon and McKenzie, Grant},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.COSIT.2024.17},
  URN =		{urn:nbn:de:0030-drops-208320},
  doi =		{10.4230/LIPIcs.COSIT.2024.17},
  annote =	{Keywords: Qualitative Spatial Logic, Soundness, Completeness}
}

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A Logic of East and West for Intervals (Short Paper)

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