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

Li, Zekai; Farjudian, Amin; Du, Heshan

doi:10.4230/LIPIcs.COSIT.2024.17

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Document Identifiers

DOI: 10.4230/LIPIcs.COSIT.2024.17
URN: urn:nbn:de:0030-drops-208320

Author Details

Zekai Li

School of Computer Science, University of Nottingham Ningbo China, China

Amin Farjudian

School of Mathematics, University of Birmingham, UK

Heshan Du

School of Computer Science, University of Nottingham Ningbo China, China

Cite AsGet BibTex

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)
https://doi.org/10.4230/LIPIcs.COSIT.2024.17

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.

Subject Classification

ACM Subject Classification

Theory of computation → Automated reasoning

Keywords

Qualitative Spatial Logic
Soundness
Completeness

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