Superposition of Qualitative Rectangles using a Quantitative Model

Takeaki Kato, Sosuke Moriguchi, Kazuko Takahashi


This paper describes an approach to qualitative problem-solving using the quantitative method in spatial reasoning. We consider the superposition of two objects, such that pre-specified parts of the objects are visible. First, we qualify an object to create a model. It is expressed as a matrix of tiles, which are either black or white depending on the visibility requirement. We use this to determine the location of two objects. This process involved quantitative treatment. We describe a sound and complete algorithm that provides quantitative solutions and implemented it as a system with a graphical user interface. Then, we extend this algorithm so that we may search for a better solution considering a qualitatively equivalent model of the objects; that is, the topological relationships between the black and white regions are identical. This approach is useful for analyzing or designing a projection of three-dimensional objects onto a two-dimensional plane, because it not only reduces the computational expense but also provides a better fit with common sense and human reasoning.


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Paper Citation

in Harvard Style

Kato T., Moriguchi S. and Takahashi K. (2017). Superposition of Qualitative Rectangles using a Quantitative Model . In Proceedings of the 9th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART, ISBN 978-989-758-220-2, pages 423-430. DOI: 10.5220/0006123404230430

in Bibtex Style

author={Takeaki Kato and Sosuke Moriguchi and Kazuko Takahashi},
title={Superposition of Qualitative Rectangles using a Quantitative Model},
booktitle={Proceedings of the 9th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,},

in EndNote Style

JO - Proceedings of the 9th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,
TI - Superposition of Qualitative Rectangles using a Quantitative Model
SN - 978-989-758-220-2
AU - Kato T.
AU - Moriguchi S.
AU - Takahashi K.
PY - 2017
SP - 423
EP - 430
DO - 10.5220/0006123404230430