What is space? Is there space when there are objects to occupy it or is there space only when there are no objects to occupy it? Can there be space without objects? These are old philosophical questions that concern the ontology of space in the philosophical sense of 'ontology' - what is the nature of space? Cognitive science in general and arti?cial intelligence in particular are less c- cerned with the nature of things than with their mental conceptualizations. In spatial cognition research we address questions like What do we know about space? How is space represented? What are the representational entities? What are the rep- sentational structures? Answers to these questions are described in what is called ontologies in arti?cial intelligence. Different tasks require different knowledge, and different representations of knowledge facilitate different ways of solving problems. In this book, Jan Oliver Wallgrn develops and investigates representational structures to support tasks of autonomous mobile robots, from the acquisition of knowledge to the use of this knowledge for navigation. The research presented is concerned with the robot mapping problem, the pr- lem of building a spatial representation of an environment that is perceived by s- sors that only provide incomplete and uncertain information; this information usually needs to be related to other imprecise or uncertain information. The routes a robot can take can be abstractly described in terms of graphs where alternative routes are represented by alternative branches in these route graphs.