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Granular Spatial Calculi of Relative Directions or Movements with Parallelism: Consistent Account (Short Paper)

Authors Reinhard Moratz, Leif Sabellek, Thomas Schneider

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Reinhard Moratz
  • Institute for Geoinformatics, University of Münster, Germany
Leif Sabellek
  • Department of Mathematics and Computer Science, University of Bremen, Germany
Thomas Schneider
  • Department of Mathematics and Computer Science, University of Bremen, Germany

Acknowledgements

We thank the anonymous reviewers for their constructive comments.

Cite As Get BibTex

Reinhard Moratz, Leif Sabellek, and Thomas Schneider. Granular Spatial Calculi of Relative Directions or Movements with Parallelism: Consistent Account (Short Paper). In 14th International Conference on Spatial Information Theory (COSIT 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 142, pp. 28:1-28:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019) https://doi.org/10.4230/LIPIcs.COSIT.2019.28

Abstract

The OPRA* calculus family, originally suggested by Frank Dylla, adds parallelism to the OPRA calculus family which is very popular in Qualitative Spatio-temporal Reasoning (QSTR). Adding parallelism enables the direct representation of parallel moving objects, which is relevant in many applications like traffic monitoring. However, it turned out that it is hard to derive a sound geometric analysis. So far no sound spatial reasoning was supported. Our new generic analysis based on combining condensed semantics lower bounds with upper bounds from algebraic mappings of related calculi already leads to a close and sound approximization. This approximization can be easily augmented with a manual analysis of few geometrically underconstrained cases and then yields a complete analysis of possible configurations in this oriented point framework. This for the first time enables sound standard QSTR constraint reasoning for the OPRA* calculus family.

Subject Classification

ACM Subject Classification
  • Computing methodologies → Spatial and physical reasoning
  • Computing methodologies → Symbolic calculus algorithms
  • Information systems → Spatial-temporal systems
Keywords
  • qualitative spatial-temporal reasoning
  • composition table
  • condensed semantics
  • homomorphic embeddings

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References

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