# Formalizing the Qualitative Superposition of Rectangles in Proof Assistant Isabelle/HOL

### Fadoua Ghourabi, Kazuko Takahashi

#### Abstract

We formalize and verify the superposition of rectangles in Isabelle/HOL. The superposition is associated with the arrangement of rectangular software windows while keeping some regions visible and other hidden. We adopt a qualitative spatial reasoning approach to represent these rectangles and the relations between their regions. The properties of the model are formally proved and show some characteristics of superposition operation. Although, this work is limited to 29 structures of rectangles, the superpositions produce hundreds of cases that are tedious to tackle in Isabelle/HOL. We also explain our strategy to optimize the proofs.

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#### Paper Citation

#### in Harvard Style

Ghourabi F. and Takahashi K. (2015). **Formalizing the Qualitative Superposition of Rectangles in Proof Assistant Isabelle/HOL** . In *Proceedings of the International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,* ISBN 978-989-758-074-1, pages 530-539. DOI: 10.5220/0005280005300539

#### in Bibtex Style

@conference{icaart15,

author={Fadoua Ghourabi and Kazuko Takahashi},

title={Formalizing the Qualitative Superposition of Rectangles in Proof Assistant Isabelle/HOL},

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

year={2015},

pages={530-539},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0005280005300539},

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 - Formalizing the Qualitative Superposition of Rectangles in Proof Assistant Isabelle/HOL

SN - 978-989-758-074-1

AU - Ghourabi F.

AU - Takahashi K.

PY - 2015

SP - 530

EP - 539

DO - 10.5220/0005280005300539