Towards Verified Construction for Planar Class of a Qualitative Spatial Representation

Sosuke Moriguchi; Mizuki Goto; Kazuko Takahashi

doi:10.29007/zzft

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Towards Verified Construction for Planar Class of a Qualitative Spatial Representation

13 pages•Published: March 27, 2016

Sosuke Moriguchi, Mizuki Goto and Kazuko Takahashi

Abstract

PLCA is a framework for qualitative spatial reasoning, using symbolic objects and relationships between them. To show construction of a PLCA expression, the second and the third authors introduced inductive constructions. They also proved that expressions obtained by inductive constructions are planar (planarity) and planar PLCA expressions can be obtained by inductive constructions (realizability). The former one is proven with Coq proof assistant, but the latter is proven with pen-and-paper.

We are currently proving the latter with Coq. We locate some oversights in the original inductive constructions and the proof. In this paper, we report these oversights, re-formalization of inductive constructions and modified proofs. We prove planarity and a base case of realizability with Coq, and induction step of realizability with Coq and pen-and-paper proof.

Keyphrases: Coq, planarity, PLCA, proof assistant, qualitative spatial reasoning

In: James H. Davenport and Fadoua Ghourabi (editors). SCSS 2016. 7th International Symposium on Symbolic Computation in Software Science, vol 39, pages 117--129

Links:	https://easychair.org/publications/paper/Zv
	https://doi.org/10.29007/zzft

BibTeX entry

@inproceedings{SCSS2016:Towards_Verified_Construction_for,
  author    = {Sosuke Moriguchi and Mizuki Goto and Kazuko Takahashi},
  title     = {Towards Verified Construction for Planar Class of a Qualitative Spatial Representation},
  booktitle = {SCSS 2016. 7th International Symposium on  Symbolic Computation in Software Science},
  editor    = {James H. Davenport and Fadoua Ghourabi},
  series    = {EPiC Series in Computing},
  volume    = {39},
  pages     = {117--129},
  year      = {2016},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {https://easychair.org/publications/paper/Zv},
  doi       = {10.29007/zzft}}

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