Construction of a Planar PLCA Expression: A Qualitative Treatment of Spatial Data

Takahashi, Kazuhiko; Goto, Mizuki; Miwa, Hiroyoshi

doi:10.1007/978-3-319-27947-3_16

Cited by 2 publications

(3 citation statements)

References 14 publications

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“…In this section, we explain the original inductive constructions introduced in [15] and the problems in the original version. After that, we introduce re-formalization of inductive constructions.…”

Section: Inductive Plcamentioning

confidence: 99%

“…Inductive constructions are defined using an inductive predicate in Coq. In the previous work [15], the predicate has three constructors, single loop, add loop and add inpath 3 . Intuitively, single loop generates an expression corresponding to a figure with only its outermost; add loop splits a region using a simple cycle; and add inpath splits a region by dividing a circuit.…”

Section: Original Inductive Constructionmentioning

confidence: 99%

“…Takahashi et al proposed a computational model of PLCA, called inductive PLCA [15]. The model provides a method for constructing expressions of PLCA, which correspond to planar figures.…”

Section: Introductionmentioning

confidence: 99%

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Towards Verified Construction for Planar Class of a Qualitative Spatial Representation

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PLCA is a framework for qualitative spatial reasoning that uses symbolic objects and the relationships between them. The second and third authors introduced inductive constructions to show construction of a PLCA expression. They also proved that expressions obtained by inductive constructions are planar (planarity) and that planar PLCA expressions can be obtained using inductive constructions (realizability). They proved the former using the Coq proof assistant, and proved the latter using a pen-and-paper proof. We tried to prove the latter using Coq, and identified some problems in the original inductive constructions and the proof. This paper reports these problems, and presents re-formalized inductive constructions and modified proofs. We were able to prove planarity and a base case of realizability with Coq, and used a pen-and-paper proof and Coq for the induction step of realizability.

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Section: Inductive Plcamentioning

confidence: 99%

Section: Original Inductive Constructionmentioning

confidence: 99%