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More is Sometimes Less: Succinctness in EL

In logics, there are many ways to represent same facts. With respect to both reasoning and cognitive complexity, some representations are significantly less efficient than others. In this paper, we investigate different means of improving the succinctness of TBoxes expressed in the lightweight description logic EL that forms a basis of some large ontologies used in practice. As a measure of size, we consider the number of references to signature elements. We investigate the problem of finding minimal equivalent representations and show that this task is NP-complete. A significant (up to triple-exponential) further improvement can be achieved by the introduction of auxiliary concept symbols. Thus, we additionally investigate the task of finding minimal representations for an ontology by extending its signature. Since arbitrary extension of the ontology with concept symbols can make the ontology unreadable, we only allow for auxiliary concepts acting as shortcuts for other concepts (EL concepts and disjunctions thereof) expressed by means of terms of the original ontology. We show that this task is also NP-complete if shortcuts represent only EL concepts, and between NP and Σ 2 , otherwise.