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Ejarque24/Extended-Q3D

Authors: Martí Ejarque and Zoe Falomir


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@misc{dagpub-supp--paper-25494-urlgithub.com-Ejarque24-Extended-Q3D,
   title = {{Ejarque24/Extended-Q3D}}, 
   author = {Ejarque, Mart{\'\i} and Falomir, Zoe},
   note = {Software (visited on 2026-09-10)},
   url = {https://github.com/Ejarque24/Extended-Q3D},
}
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An Extended Qualitative Model for Reasoning About 3D Objects Using Depth and Different Perspectives

Authors: Martí Ejarque and Zoe Falomir

Published in: LIPIcs, Volume 393, 17th International Conference on Spatial Information Theory (COSIT 2026)


Abstract
Reconstructing a three-dimensional structure from partial two-dimensional views requires spatial reasoning. This paper presents the EQ3D, a dimension-agnostic extension of the Qualitative 3D (Q3D) model that generalises qualitative volumetric reasoning to arbitrary H× W× L configurations. EQ3D preserves symbolic depth representations while incorporating adjacent-view propagation rules that increase cross-view inference opportunities. Implemented in SWI-Prolog as a fully declarative pipeline, EQ3D infers hidden views from three orthographic Front-Right-Up views, producing correct inferred cells for the Q3D-Dataset which includes 24 objects of varying size and shape, while ambiguous cells remain explicitly undetermined. Coverage of hidden structure ranges from 26.85% to 82.67%, demonstrating that while inference remains logically sound, the proportion of determinable volume is inherently configuration-dependent. EQ3D provides an interpretable symbolic framework for qualitative 3D reasoning that scales across resolutions without size-specific adaptation.

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Martí Ejarque and Zoe Falomir. An Extended Qualitative Model for Reasoning About 3D Objects Using Depth and Different Perspectives. In 17th International Conference on Spatial Information Theory (COSIT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 393, pp. 5:1-5:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)


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@InProceedings{ejarque_et_al:LIPIcs.COSIT.2026.5,
  author =	{Ejarque, Mart{\'\i} and Falomir, Zoe},
  title =	{{An Extended Qualitative Model for Reasoning About 3D Objects Using Depth and Different Perspectives}},
  booktitle =	{17th International Conference on Spatial Information Theory (COSIT 2026)},
  pages =	{5:1--5:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-438-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{393},
  editor =	{Timpf, Sabine and Filomena, Gabriele and Kapaj, Armand and Zhu, Rui and Giudice, Nicholas A. and Manley, Ed},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.COSIT.2026.5},
  URN =		{urn:nbn:de:0030-drops-275490},
  doi =		{10.4230/LIPIcs.COSIT.2026.5},
  annote =	{Keywords: qualitative spatial reasoning, spatial cognition, first order logics, three-dimensional information, perspectives, object perception, SWI-Prolog}
}

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