Document Open Access Logo

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

Authors Zekai Li , Amin Farjudian , Heshan Du

PDF

File

Thumbnail PDF
PDF
LIPIcs.COSIT.2024.17.pdf
  • Filesize: 0.76 MB
  • 8 pages

Document Identifiers

Subject Classification

ACM Subject Classification
  • Theory of computation → Automated reasoning
Keywords
  • Qualitative Spatial Logic
  • Soundness
  • Completeness

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

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.

Cite As Get 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

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

References

  1. James F. Allen. Maintaining Knowledge about Temporal Intervals. Communications of the ACM, 26(11):832-843, 1983. URL: https://doi.org/10.1145/182.358434.
  2. Philippe Balbiani, Jean-François Condotta, and Luis Fariñas del Cerro. A Model for Reasoning about Bidimensional Temporal Relations. In Proceedings of the 6th International Conference on Principles of Knowledge Representation and Reasoning (KR), pages 124-130, 1998. Google Scholar
  3. Nikolaj S. Bjørner, Clemens Eisenhofer, and Laura Kovács. Satisfiability modulo custom theories in Z3. In Proceedings of the 24th International Conference on Verification, Model Checking, and Abstract Interpretation (VMCAI), volume 13881 of Lecture Notes in Computer Science, pages 91-105. Springer, 2023. Google Scholar
  4. Ronald J. Brachman and Hector J. Levesque. Knowledge Representation and Reasoning. Elsevier, 2004. Google Scholar
  5. Heshan Du, Natasha Alechina, Amin Farjudian, Brian Logan, Can Zhou, and Anthony G Cohn. A logic of east and west. Journal of Artificial Intelligence Research, 76:527-565, 2023. Google Scholar
  6. Jérôme Euzenat and Pavel Shvaiko. Ontology Matching, Second Edition. Springer, 2013. Google Scholar
  7. Nikolaos Karalis, Georgios M. Mandilaras, and Manolis Koubarakis. Extending the YAGO2 knowledge graph with precise geospatial knowledge. In Proceedings of the 18th International Semantic Web Conference (ISWC), volume 11779 of Lecture Notes in Computer Science, pages 181-197. Springer, 2019. Google Scholar
  8. Robert E. Shostak. Deciding Linear Inequalities by Computing Loop Residues. Journal of the ACM, 28(4):769-779, 1981. Google Scholar
  9. Spiros Skiadopoulos and Manolis Koubarakis. Composing cardinal direction relations. Artificial Intelligence, 152(2):143-171, 2004. Google Scholar
  10. Spiros Skiadopoulos and Manolis Koubarakis. On the consistency of cardinal direction constraints. Artificial Intelligence, 163(1):91-135, 2005. Google Scholar
  11. Nicolas Tempelmeier and Elena Demidova. Linking openstreetmap with knowledge graphs - link discovery for schema-agnostic volunteered geographic information. Future Gener. Comput. Syst., 116:349-364, 2021. Google Scholar
  12. Marc B. Vilain and Henry A. Kautz. Constraint Propagation Algorithms for Temporal Reasoning. In Proceedings of the 5th National Conference on Artificial Intelligence (AAAI), pages 377-382, 1986. Google Scholar
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2025 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact