Dualistic Ontologies

To effectively use and share knowledge among AI systems, a formal specification of the representation of their shared domain of discourse – called an ontology – is indispensable. In this paper we demonstrate the role of dualistic ontologies in human activities such as searching, in-depth exploration and browsing. We start with the introduction of a formal definition of dualistic ontologies, based on a dual view on the universe of discourse. Then we relate this formal definition to three different (well known) kinds of ontologies, based on the vector model, on formal concept analysis and on fuzzy logic respectively. The vector model leads to concepts derived by latent semantic indexing using the singular value decomposition. Both the set model as the fuzzy set model lead to Formal Concept Analysis, in which the fuzzy set model is equipped with a parameter that controls the fine-grainedness of the resulting concepts. We discuss the relation between the resulting systems of concepts. Finally, we demonstrate the use of this theory by introducing the dual search engine. We show how this search engine can be employed to support the human activities addressed above.