Implicit spatial reference systems using proximity and aligment knowledge

In this paper, we explore the situation where no cardinal directions or globally available orientations are available and no metric estimates are given. This corresponds to the way many people perceive their environment and carry out spatial reasoning tasks. We consider three kinds of locally available information – proximity (nearest neighbor), relevance (different sets of neighbors) and distribution (alignments) – and we limit our interest to a universe of point objects. We show how the theory of manifolds and sheaves can be applied to the problem of combining locally available information of a qualitative nature into a global model of an environmental space. We then explore the limitations of the resulting global model if information capture is incomplete or uncertain. Finally, we note that some indeterminacy in the global model does not entail difficulties for a user, provided the reasoning task is appropriately constrained or appropriate additional information is used, such as an external reference.