Spatial reasoning about qualitative shape compositions: Composing Qualitative Lengths and Angles

Zoe Falomir, Albert Pich, Vicent Costa

Research output: Contribution to journalArticleResearch

1 Citation (Scopus)


© 2019, Springer Nature Switzerland AG. 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). 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.
Original languageEnglish
JournalAnnals of Mathematics and Artificial Intelligence
Publication statusPublished - 1 Jan 2019


  • Composition tables
  • Correctness
  • Geometry
  • Qualitative angles
  • Qualitative lengths
  • Qualitative reasoning
  • Qualitative representation
  • Shapes
  • Spatial reasoning


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