Rational Region-Based Affine Logic of the Real Plane

Abstract

The region-based spatial logics, where variables are set to range over certain subsets of geometric space, are the focal point of the qualitative spatial reasoning, a subfield of the KR&R research area. A lot of attention has been devoted to developing the topological spatial logics, leaving other systems relatively underexplored. We are concerned with a specific example of a region-based affine spatial logic. Building on the previous results on spatial logics with convexity, we axiomatise the theory of M = 〈 ROQ (R 2 ), conv M , ≤ M 〉, where ROQ (R 2 ) is the set of regular open rational polygons of the real plane; conv M is the convexity property and ≤ M is the inclusion relation. The axiomatisation uses two infinitary rules of inference and a number of axiom schemas.