Abstract
AbstractUnification has been introduced in Description Logic (DL) as a means to detect redundancies in ontologies. In particular, it was shown that testing unifiability in the DL $$\mathcal{E}\mathcal{L}$$
E
L
is an NP-complete problem, and this result has been extended in several directions. Surprisingly, it turned out that the complexity increases to PSpace if one disallows the use of the top concept in concept descriptions. Motivated by features of the medical ontology SNOMED CT, we extend this result to a setting where the top concept is disallowed, but there is a background ontology consisting of restricted forms of concept and role inclusion axioms. We are able to show that the presence of such axioms does not increase the complexity of unification without top, i.e., testing for unifiability remains a PSpace-complete problem.
Publisher
Springer Nature Switzerland
Reference29 articles.
1. Baader, F., Binh, N.T., Borgwardt, S., Morawska, B.: Unification in the description logic $$\cal{EL}$$ without the top concept. In: Bjørner, N., Sofronie-Stokkermans, V. (eds.) CADE 2011. LNCS (LNAI), vol. 6803, pp. 70–84. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-22438-6_8
2. Baader, F., Borgwardt, S., Morawska, B.: Extending unification in $$\cal{EL}$$ towards general tboxes. In: Principles of Knowledge Representation and Reasoning: Proceedings of the Thirteenth International Conference (KR 2012), Rome, 10–14 June 2012. AAAI Press (2012)
3. Baader, F., Borgwardt, S., Morawska, B.: A goal-oriented algorithm for unification in $$\cal{ELH}_{R+}$$ w.r.t. cycle-restricted ontologies. In: Thielscher, M., Zhang, D. (eds.) AI 2012. LNCS (LNAI), vol. 7691, pp. 493–504. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-35101-3_42
4. Baader, F., Borgwardt, S., Morawska, B.: A goal-oriented algorithm for unification in $$\cal{ELH}_{R^+}$$ w.r.t. cycle-restricted ontologies. LTCS-Report 12-05, Chair for Automata Theory, Institute for Theoretical Computer Science, Technische Universität Dresden, Dresden (2012). https://doi.org/10.25368/2022.189
5. Baader, F., Borgwardt, S., Morawska, B.: SAT encoding of unification in $$\cal{ELH}_{{R}^+}$$ w.r.t. cycle-restricted ontologies. In: Gramlich, B., Miller, D., Sattler, U. (eds.) IJCAR 2012. LNCS (LNAI), vol. 7364, pp. 30–44. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-31365-3_5