Exceptions in Ontologies

This chapter is a contribution to the study of formal ontologies. It addresses the problem of atypical entities in ontologies. The authors propose a new model of knowledge representation by combining ontologies and topology. In order to represent atypical entities in ontologies, the four topological operators of interior, exterior, border and closure are introduced. These operators allow to specify whether an entity, belonging to a class, is typical or not. The authors define a system of topological inclusion and membership relations into the ontology formalism, by adapting the four topological operators with the help of their mathematical properties. These properties are used as a set of axioms which allows to define the topological inclusion and membership relations. Further, the authors define combinations of the operators of interior, exterior, border and closure that allow the construction of an algebra. They model is implemented in AnsProlog, a recent logic programming language that allows negative predicates in inference rules.