Algebraic Properties of Qualitative Spatio-Temporal Calculi

Qualitative spatial and temporal reasoning is based on so-called qualitative calculi. Algebraic properties of these calculi have several implications on reasoning algorithms. But what exactly is a qualitative calculus? And to which extent do the qualitative calculi proposed meet these demands? The literature provides various answers to the first question but only few facts about the second. In this paper we identify the minimal requirements to binary spatio-temporal calculi and we discuss the relevance of the according axioms for representation and reasoning. We also analyze existing qualitative calculi and provide a classification involving different notions of a relation algebra.Comment: COSIT 2013 paper including supplementary materia

Specification of an ontology for route graphs

This paper describes the general concept of Route Graphs, to be used for navigation by various agents in a variety of scenarios. We introduce the concept of an ontology and describe the modelling of general graphs as an example. This approach is then applied to define a “light-weight ” ontology of Route Graphs in an indoors environment, giving at first just a taxonomy of (sub)classes and relations between them, as well as to other (spatial) ontologies. Finally, we show how to formalise ontologies using a First Order Logic approach, and give an outline of how to develop actual data structures and algorithms for Route Graphs