Towards Verified Construction for Planar Class of a Qualitative Spatial Representation

Abstract

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.