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Spatial reasoning about qualitative shape compositions

Composing Qualitative Lengths and Angles

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Abstract

Shape composition is a challenge in spatial reasoning. Qualitative Shape Descriptors (QSD) have proven to be rotation and location invariant, which make them useful in spatial reasoning tests. QSD uses qualitative representations for angles and lengths, but their composition operations have not been defined before. In this paper, the Qualitative Model for Angles (QMAngles) and the Qualitative Model for Lengths (QMLengths) are presented in detail by describing their arity, reference systems and operators. Their operators are defined taking the well-known temporal model by Allen (Commun. ACM 26(11), 832–843 (1983). https://doi.org/10.1145/182.358434) as a reference. Moreover, composition tables are built, and the composition relations of qualitative angles and lengths are proved using their geometric counterparts. The correctness of these composition tables is also proved computationally using a logic program implemented using Swi-Prolog.

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Notes

  1. Bremen Spatial Cognition Centre:http://bscc.spatial-cognition.de/

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Acknowledgements

The funding and support by the Bremen Spatial Cognition CenterFootnote 1 (BSCC), the University of Bremen under project Cognitive Qualitative Descriptions and Applications (CogQDA), the Erasmus + Internship program, the grant FI-2017 (Generalitat de Catalunya and the European Social Fund) and the Young European Research Universities (YERUN) Mobility awards (first edition 2017/2018, and second edition 2018/2019) are all gratefully acknowledged. The authors also acknowledge discussions with Ramon Garcia-Pou. And they also thank the reviewers for their comments, which helped to improve this paper.

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Authors and Affiliations

  1. Bremen Spatial Cognition Centre, University of Bremen, Bremen, Germany

    Zoe Falomir & Albert Pich

  2. Department of Philosophy, Universitat Autònoma of Barcelona, Catalonia, Spain

    Vicent Costa

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  1. Zoe Falomir
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Correspondence to Zoe Falomir.

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Falomir, Z., Pich, A. & Costa, V. Spatial reasoning about qualitative shape compositions. Ann Math Artif Intell 88, 589–621 (2020). https://doi.org/10.1007/s10472-019-09637-7

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