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 defined
as an abduction task, described in procedural terms according to the current
implementation of the SSH. In this paper we define 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.