# A Qualitative Representation of a Figure and Construction of Its Planar Class

### Kazuko Takahashi, Mizuki Goto, Hiroyoshi Miwa

#### Abstract

PLCA is a framework for qualitative spatial reasoning. It provides a symbolic expression of spatial entities and allows reasoning on this expression. A figure is represented using the objects used to construct it, that is, points, lines, circuits and areas, as well as the relationships between them without numerical data. The figure is identified by the patterns of connection between the objects. For a given PLCA expression, the conditions for planarity, that is, an existence of the corresponding figure on a two-dimensional plane, have been shown; however, the construction of such a PLCA expression has not been discussed. In this paper, we describe a method of constructing such expressions inductively, and prove that the resulting class coincides with that of the planar PCLA. The part of the proof is implemented using a proof assistant Coq.

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#### Paper Citation

#### in Harvard Style

Takahashi K., Goto M. and Miwa H. (2015). **A Qualitative Representation of a Figure and Construction of Its Planar Class** . In *Proceedings of the International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,* ISBN 978-989-758-074-1, pages 204-212. DOI: 10.5220/0005263102040212

#### in Bibtex Style

@conference{icaart15,

author={Kazuko Takahashi and Mizuki Goto and Hiroyoshi Miwa},

title={A Qualitative Representation of a Figure and Construction of Its Planar Class},

booktitle={Proceedings of the International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,},

year={2015},

pages={204-212},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0005263102040212},

isbn={978-989-758-074-1},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,

TI - A Qualitative Representation of a Figure and Construction of Its Planar Class

SN - 978-989-758-074-1

AU - Takahashi K.

AU - Goto M.

AU - Miwa H.

PY - 2015

SP - 204

EP - 212

DO - 10.5220/0005263102040212