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Cut-Free ExpTime Tableaux for Checking Satisfiability of a Knowledge Base in the Description Logic \(\mathcal{ALCI}\)

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Foundations of Intelligent Systems (ISMIS 2011)

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Abstract

We give the first direct cut-free ExpTime (optimal) tableau decision procedure, which is not based on transformation or on the pre-completion technique, for checking satisfiability of a knowledge base in the description logic \(\mathcal{ALCI}\).

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References

  1. Ding, Y., Haarslev, V., Wu, J.: A new mapping from \(\mathcal{ALCI}\) to \(\mathcal{ALC}\). In: Proceedings of Description Logics (2007)

    Google Scholar 

  2. De Giacomo, G., Lenzerini, M.: TBox and ABox reasoning in expressive description logics. In: Aiello, L.C., Doyle, J., Shapiro, S.C. (eds.) Proceedings of KR 1996, pp. 316–327. Morgan Kaufmann, San Francisco (1996)

    Google Scholar 

  3. Goré, R.P., Nguyen, L.A.: EXPTIME tableaux with global caching for description logics with transitive roles, inverse roles and role hierarchies. In: Olivetti, N. (ed.) TABLEAUX 2007. LNCS (LNAI), vol. 4548, pp. 133–148. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  4. Goré, R., Widmann, F.: Sound global state caching for ALC with inverse roles. In: Giese, M., Waaler, A. (eds.) TABLEAUX 2009. LNCS, vol. 5607, pp. 205–219. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  5. Goré, R., Widmann, F.: Optimal and cut-free tableaux for propositional dynamic logic with converse. In: Giesl, J., Hähnle, R. (eds.) IJCAR 2010. LNCS, vol. 6173, pp. 225–239. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  6. Horrocks, I., Sattler, U.: Description logics - basics, applications, and more. In: Tutorial Given at ECAI-2002, http://www.cs.man.ac.uk/~horrocks/Slides/ecai-handout.pdf

  7. Nguyen, L.A.: An efficient tableau prover using global caching for the description logic {ALC}. Fundamenta Informaticae 93(1-3), 273–288 (2009)

    MathSciNet  MATH  Google Scholar 

  8. Nguyen, L.A.: The long version of the current paper (2011), http://www.mimuw.edu.pl/~nguyen/alci-long.pdf

  9. Nguyen, L.A., Szałas, A.: expTime tableaux for checking satisfiability of a knowledge base in the description logic \(\mathcal{ALC}\). In: Nguyen, N.T., Kowalczyk, R., Chen, S.-M. (eds.) ICCCI 2009. LNCS(LNAI), vol. 5796, pp. 437–448. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  10. Nguyen, L.A., Szałas, A.: An optimal tableau decision procedure for Converse-PDL. In: Nguyen, N.-T., Bui, T.-D., Szczerbicki, E., Nguyen, N.-B. (eds.) Proceedings of KSE 2009, pp. 207–214. IEEE Computer Society, Los Alamitos (2009)

    Google Scholar 

  11. Nguyen, L.A., Szałas, A.: A tableau calculus for regular grammar logics with converse. In: Schmidt, R.A. (ed.) CADE-22. LNCS(LNAI), vol. 5663, pp. 421–436. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  12. Nguyen, L.A., Szałas, A.: Checking consistency of an ABox w.r.t. global assumptions in PDL. Fundamenta Informaticae 102(1), 97–113 (2010)

    MathSciNet  MATH  Google Scholar 

  13. Nguyen, L.A., Szałas, A.: Tableaux with global caching for checking satisfiability of a knowledge base in the description logic \(\mathcal{SH}\). T. Computational Collective Intelligence 1, 21–38 (2010)

    MATH  Google Scholar 

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Nguyen, L.A. (2011). Cut-Free ExpTime Tableaux for Checking Satisfiability of a Knowledge Base in the Description Logic \(\mathcal{ALCI}\) . In: Kryszkiewicz, M., Rybinski, H., Skowron, A., Raś, Z.W. (eds) Foundations of Intelligent Systems. ISMIS 2011. Lecture Notes in Computer Science(), vol 6804. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21916-0_50

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  • DOI: https://doi.org/10.1007/978-3-642-21916-0_50

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-21915-3

  • Online ISBN: 978-3-642-21916-0

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