Towards a Mathematical Theory for Snapshot and Temporal Formal Ontologies

Abstract

In order to achieve interoperability of GIS, the meaning of the data must be expressed in a compatible description. Formal methods to describe the ontology of data are increasingly used, but the detail of their definitions are debated. In this paper I investigate the mathematical structure of formal ontologies as they are the background for ontology languages like OWL, which are increasingly used in GIS. I separate formal aspects of the ontology languages from possible interpretations of the formulae in light of philosophical position. The paper gives formal description of a static and a temporal formal ontology. This clarifies what are assumptions (i.e., ontological commitments) and what are consequences of these. A formalized treatment leads to a consistent formal ontology and is the precondition for the integration of ontological descriptions of geographic data. The analysis shows that most of the important restrictions in ontologies can be expressed only in a temporal ontology and they are often related to the question, which processes are included in the temporal ontology.