Towards a general theory of topological maps

AbstractWe present a general theory of topological maps whereby sensory input, topological and local metrical information are combined to define the topological maps explaining such information. Topological maps correspond to the minimal models of an axiomatic theory describing the relationships between the different sources of information explained by a map. We use a circumscriptive theory to specify the minimal models associated with this representation.The theory here proposed is independent of the exploration strategy the agent follows when building a map. We provide an algorithm to calculate the models of the theory. This algorithm supports different exploration strategies and facilitates map disambiguation when perceptual aliasing arises