Knowledge Representation for Distances and Orientations of Regions

From the perspective of cognitive informatics (CI), this paper proposes internal relations between distance and orientation knowledge of extended objects, and presents a formal representation of spatial knowledge. The connection relation is taken as primitive. Notions of near extension regions and the nearer predicate are developed. Distance relations between extended objects are understood as degrees of the near extension from one object to the other. Orientation relations are understood as distance comparison from one object to the sides of the other object. Therefore, distance and orientation relations can be internally related through the connection relation. The notion of the fiat projection is presented to model the mental formation of the deictic orientation reference framework. This paper introduces a new axiom to govern the connection relation in the literature and presents examples to show diagrammatically the internal relations between distance and orientation relations of extended objects.