Abstract
We develop a resolution-based method for forgetting concept and role symbols in \(\mathcal{ALCH}\) ontologies, or for computing uniform interpolants in \(\mathcal{ALCH}\). Uniform interpolants use only a restricted set of symbols, while preserving logical consequences of the original ontology involving these symbols. While recent work towards practical methods for uniform interpolation in expressive description logics limits attention to forgetting concept symbols, we believe most applications would benefit from the possibility to forget both role and concept symbols. We focus on the description logic \(\mathcal{ALCH}\), which allows for the formalisation of role hierarchies. Our approach is based on a recently developed resolution-based calculus for forgetting concept symbols in \(\mathcal{ALC}\) ontologies, which we extend by redundancy elimination techniques to make it practical for larger ontologies. Experiments on \(\mathcal{ALCH}\) fragments of real life ontologies suggest that our method is applicable in a lot of real-life applications.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Ackermann, W.: Untersuchungen über das Eliminationsproblem der mathematischen Logik. Mathematische Annalen 110(1), 390–413 (1935)
Calvanese, D., Giacomo, G.D., Lenzerini, M.: Reasoning in expressive description logics with fixpoints based on automata on infinite trees. In: Proc. IJCAI 1999, pp. 84–89. Morgan Kaufmann (1999)
Gabbay, D., Ohlbach, H.J.: Quantifier elimination in second-order predicate logic. In: Proc. KR 1992, pp. 425–435. Morgan Kaufmann (1992)
Gabbay, D.M., Schmidt, R.A., Szalas, A.: Second Order Quantifier Elimination: Foundations, Computational Aspects and Applications. College Publ. (2008)
Grau, B.C., Motik, B.: Reasoning over ontologies with hidden content: The import-by-query approach. J. Artificial Intelligence Research 45, 197–255 (2012)
Herzig, A., Mengin, J.: Uniform interpolation by resolution in modal logic. In: Hölldobler, S., Lutz, C., Wansing, H. (eds.) JELIA 2008. LNCS (LNAI), vol. 5293, pp. 219–231. Springer, Heidelberg (2008)
Horridge, M., Parsia, B., Sattler, U.: The state of bio-medical ontologies. Bio-Ontologies 2011 (2011)
Konev, B., Walther, D., Wolter, F.: Forgetting and uniform interpolation in large-scale description logic terminologies. In: Proc. IJCAI 2009, pp. 830–835 (2009)
Koopmann, P., Schmidt, R.A.: Forgetting concept and role symbols in \(\mathcal{ALCH}\)-ontologies. Technical Report (2013), http://www.cs.man.ac.uk/~koopmanp
Koopmann, P., Schmidt, R.A.: Implementation and evaluation of forgetting in \(\mathcal{ALC}\)-ontologies. In: Proc. WoMO 2013. CEUR-WS.org (2013)
Koopmann, P., Schmidt, R.A.: Uniform interpolation of \(\mathcal{ALC}\)-ontologies using fixpoints. In: Fontaine, P., Ringeissen, C., Schmidt, R.A. (eds.) FroCoS 2013. LNCS (LNAI), vol. 8152, pp. 87–102. Springer, Heidelberg (2013)
Ludwig, M., Konev, B.: Towards practical uniform interpolation and forgetting for \(\mathcal{ALC}\) TBoxes. In: Proc. DL 2013, pp. 377–389. CEUR-WS.org (2013)
Lutz, C., Seylan, I., Wolter, F.: An automata-theoretic approach to uniform interpolation and approximation in the description logic \(\mathcal{EL}\). In: Proc. KR 2012. AAAI Press (2012)
Lutz, C., Wolter, F.: Foundations for uniform interpolation and forgetting in expressive description logics. In: Proc. IJCAI 2011, pp. 989–995. AAAI Press (2011)
Nikitina, N.: Forgetting in general \(\mathcal{EL}\) terminologies. In: Proc. DL 2011. CEUR-WS.org. (2011)
Nonnengart, A., Szałas, A.: A fixpoint approach to second-order quantifier elimination with applications to correspondence theory. In: Logic at Work, pp. 307–328. Springer (1999)
Sattler, U., Schneider, T., Zakharyaschev, M.: Which kind of module should I extract? In: Proc. DL 2009. CEUR-WS.org (2009)
Shearer, R., Motik, B., Horrocks, I.: HermiT: A highly-efficient OWL reasoner. In: Proc. OWLED 2008, pp. 26–27. CEUR-WS.org (2008)
Szałas, A.: Second-order reasoning in description logics. J. Appl. Non-Classical Logics 16(3-4), 517–530 (2006)
Wang, K., Wang, Z., Topor, R., Pan, J.Z., Antoniou, G.: Eliminating concepts and roles from ontologies in expressive descriptive logics. Computational Intelligence (2012)
Wang, Z., Wang, K., Topor, R., Zhang, X.: Tableau-based forgetting in \(\mathcal{ALC}\) ontologies. In: Proc. ECAI 2010, pp. 47–52. IOS Press (2010)
Wang, Z., Wang, K., Topor, R.W., Pan, J.Z.: Forgetting for knowledge bases in DL-Lite. Ann. Math. Artif. Intell. 58(1-2), 117–151 (2010)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Koopmann, P., Schmidt, R.A. (2013). Forgetting Concept and Role Symbols in \(\mathcal{ALCH}\)-Ontologies. In: McMillan, K., Middeldorp, A., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2013. Lecture Notes in Computer Science, vol 8312. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45221-5_37
Download citation
DOI: https://doi.org/10.1007/978-3-642-45221-5_37
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-45220-8
Online ISBN: 978-3-642-45221-5
eBook Packages: Computer ScienceComputer Science (R0)