Abstract
The paper presents a tableau calculus with several refinements for reasoning in the description logic \(\mathcal{SHOI}\). The calculus uses non-standard rules for dealing with TBox statements. Whereas in existing tableau approaches a fixed rule is used for dealing with TBox statements, we use a dynamically generated set of refined rules. This approach has become practical because reasoners with flexible sets of rules can be generated with the tableau prover generation prototype MetTel. We also define and investigate variations of the unrestricted blocking mechanism in which equality reasoning is realised by ordered rewriting and the application of the blocking rule is controlled by excluding its application to a fixed, finite set of individual terms. Reasoning with the unique name assumption and excluding ABox individuals from the application of blocking can be seen as two separate instances of the latter. Experiments show the refinements lead to fewer rule applications and improved performance.
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References
Alenda, R., Olivetti, N., Schwind, C., Tishkovsky, D.: Tableau calculi for \(\mathcal{CSL}\) over minspaces. In: Dawar, A., Veith, H. (eds.) CSL 2010. LNCS, vol. 6247, pp. 52–66. Springer, Heidelberg (2010)
Baader, F., Sattler, U.: An overview of tableau algorithms for description logics. Studia Logica 69(1), 5–40 (2001)
Bolander, T., Blackburn, P.: Termination for hybrid tableaus. J. Logic Comput. 17(3), 517–554 (2007)
Cialdea Mayer, M., Cerrito, S.: Nominal substitution at work with the global and converse modalities. In: Proc. AiML-8, pp. 57–74. College Publ. (2010)
Duc, C.L., Lamolle, M.: Decidability of description logics with transitive closure of roles in concept and role inclusion axioms. In: Proc. DL 2010. CEUR Workshop Proceedings, vol. 573 (2010)
Fitting, M.: Proof methods for modal and intuitionistic logics. Kluwer (1983)
Horridge, M., Bechhofer, S.: The OWL API: A Java API for OWL ontologies. Semantic Web 2(1), 11–21 (2011)
Horrocks, I., Kutz, O., Sattler, U.: The even more irresistible SROIQ. In: Proc. KR 2006, pp. 57–67. AAAI Press (2006)
Horrocks, I., Sattler, U.: A description logic with transitive and inverse roles and role hierarchies. J. Logic Comput. 9(3), 385–410 (1999)
Horrocks, I., Sattler, U.: A tableau decision procedure for SHOIQ. J. Automat. Reasoning 39(3), 249–276 (2007)
Horrocks, I., Sattler, U., Tobies, S.: Practical reasoning for expressive description logics. In: Ganzinger, H., McAllester, D., Voronkov, A. (eds.) LPAR 1999. LNCS, vol. 1705, pp. 161–180. Springer, Heidelberg (1999)
Khodadadi, M., Schmidt, R.A., Tishkovsky, D.: An abstract tableau calculus for the description logic SHOI using unrestricted blocking and rewriting. In: Proc. DL 2012. CEUR Workshop Proceedings, vol. 846, pp. 224–234 (2012)
Khodadadi, M., Schmidt, R.A., Tishkovsky, D.: A refined tableau calculus with controlled blocking for the description logic SHOI (2013), http://www.mettel-prover.org/papers/controlled.pdf
Khodadadi, M., Schmidt, R.A., Tishkovsky, D.: A refined tableau calculus with controlled blocking for the description logic SHOI. To Appear in Proc. DL 2013. CEUR Workshop Proceedings (2013)
Matentzoglu, N., Bail, S., Parsia, B.: A corpus of OWL DL ontologies. To Appear in Proc. DL 2013. CEUR Workshop Proceedings (2013)
Schmidt, R.A., Tishkovsky, D.: Using tableau to decide expressive description logics with role negation. In: Aberer, K., et al. (eds.) ISWC/ASWC 2007. LNCS, vol. 4825, pp. 438–451. Springer, Heidelberg (2007)
Schmidt, R.A., Tishkovsky, D.: A general tableau method for deciding description logics, modal logics and related first-order fragments. In: Armando, A., Baumgartner, P., Dowek, G. (eds.) IJCAR 2008. LNCS (LNAI), vol. 5195, pp. 194–209. Springer, Heidelberg (2008)
Schmidt, R.A., Tishkovsky, D.: Automated synthesis of tableau calculi. Logical Methods in Comput. Sci. 7(2), 1–32 (2011)
Schmidt, R.A., Tishkovsky, D.: Using tableau to decide description logics with full role negation and identity. arXiv e-Print, abs/1208.1476 (2012)
Tishkovsky, D., Schmidt, R.A.: Refinement in the tableau synthesis framework. arXiv e-Print, abs/1305.3131 (2013)
Tishkovsky, D., Schmidt, R.A., Khodadadi, M.: Mettel2: Towards a tableau prover generation platform. In: Proc. PAAR 2012. EasyChair Proceedings (2012)
Tishkovsky, D., Schmidt, R.A., Khodadadi, M.: The tableau prover generator MetTeL2. In: del Cerro, L.F., Herzig, A., Mengin, J. (eds.) JELIA 2012. LNCS, vol. 7519, pp. 492–495. Springer, Heidelberg (2012)
TONES. The tones ontology repository (March 5, 2013)
Tsarkov, D., Horrocks, I.: FaCT++ description logic reasoner: System description. In: Furbach, U., Shankar, N. (eds.) IJCAR 2006. LNCS (LNAI), vol. 4130, pp. 292–297. Springer, Heidelberg (2006)
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Khodadadi, M., Schmidt, R.A., Tishkovsky, D. (2013). A Refined Tableau Calculus with Controlled Blocking for the Description Logic \(\mathcal{SHOI}\) . In: Galmiche, D., Larchey-Wendling, D. (eds) Automated Reasoning with Analytic Tableaux and Related Methods. TABLEAUX 2013. Lecture Notes in Computer Science(), vol 8123. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40537-2_17
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DOI: https://doi.org/10.1007/978-3-642-40537-2_17
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