Implicit Constraints for Qualitative Spatial and Temporal Reasoning

Qualitative information about spatial or temporal entities is represented by specifying qualitative relations between these entities. It is then possible to apply qualitative reasoning methods for tasks such as checking consistency of the given information, deriving previously unknown information or answering queries. Depending on the kind of information that is represented, qualitative reasoning methods might lead to incorrect results, and it is a topic of ongoing research efforts to determine when and why this occurs. In this paper we present two possible explanations for this behaviour: (1) the existence of implicit entities that we do not explicitly represent; (2) the existence of implicit constraints that have to be satisfied, but which are not explicitly represented. We show that both of these can lead to undetected inconsistencies. By making these implicit entities and constraints explicit, and by including them in the qualitative representation, we are able to solve problems that could not be solved qualitatively before. We present different examples of implicit entities and implicit constraints and an algorithm for solving them.