A Neo-Topological Approach to Reasoning on Ontologies with Exceptions and Comparison with Defeasible Description Logics

This article compares Defeasible Description Logics (DDL) and Topological Approach to reason on Ontologies with exceptions. DDL is integration between Description Logics and Defeasible Logics to deal with monotonic and non-monotonic parts of the knowledge bases respectively. Topological approach tries to reason on inconsistent knowledge bases using the conventional topological operators e.g., interior, exterior, border and closure. We develop neo-Topology based on topological operators and we make major development and improvements of current Topological approach by properly introducing the ``Thickness Border'' with strong inference rules. We proof the validity of the inference rules using set operations. We demonstrate both approaches with appropriate example. We show the advantages and disadvantages of both approaches.