Relational reasoning in the region connection calculus

TL;DR

This paper explores the algebraic properties of the Region Connection Calculus (RCC), revealing that its contact relation algebra is not atomic complete and providing a representation using the complemented closed disk algebra.

Contribution

It demonstrates the non-atomic completeness of RCC's contact relation algebra and offers a representation via complemented closed disk algebra.

Findings

CRA of certain RCC models is not atomic complete

RCC models satisfy RCC11 composition table

Complemented closed disk algebra represents RCC11 relation algebra

Abstract

This paper is mainly concerned with the relation-algebraical aspects of the well-known Region Connection Calculus (RCC). We show that the contact relation algebra (CRA) of certain RCC model is not atomic complete and hence infinite. So in general an extensional composition table for the RCC cannot be obtained by simply refining the RCC8 relations. After having shown that each RCC model is a consistent model of the RCC11 CT, we give an exhaustive investigation about extensional interpretation of the RCC11 CT. More important, we show the complemented closed disk algebra is a representation for the relation algebra determined by the RCC11 table. The domain of this algebra contains two classes of regions, the closed disks and closures of their complements in the real plane.