Towards a formalization of the Spatial Semantic Hierarchy

The Spatial Semantic Hierarchy (SSH) comprises a set of distinct representations of space, each with its own ontology, each with its own mathematical foundation, and each abstracted from the levels below it. In particular, the SSH topological level is abstracted from the SSH causal level. The method used to abstract the SSH topological level has usually been dened as an abduction task, described in procedural terms according to the current implementation of the SSH. In this paper we de ne the circumscriptive theories associated with the SSH causal and topological levels. These theories are used to formalize the SSH abduction task and prove our implementation correct. Moreover, these theories show how topological information is used to dictate spatial distinctions that cannot be derived from causal information alone.