Advertisement

An Automata View to Goal-Directed Methods

  • Lisa HutschenreiterEmail author
  • Rafael Peñaloza
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10168)

Abstract

Consequence-based and automata-based algorithms encompass two families of approaches that have been thoroughly studied as reasoning methods for many logical formalisms. While automata are useful for finding tight complexity bounds, consequence-based algorithms are typically simpler to describe, implement, and optimize. In this paper, we show that consequence-based reasoning can be reduced to the emptiness test of an appropriately built automaton. Thanks to this reduction, one can focus on developing efficient consequence-based algorithms, obtaining complexity bounds and other benefits of automata methods for free.

Keywords

Description Logic Derivation Tree Rule Application Label Tree Tree Automaton 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Baader, F., Brandt, S., Lutz, C.: Pushing the \(\cal{EL}\) envelope. In: Proceedings of IJCAI 2005. Morgan Kaufmann, Edinburgh (2005)Google Scholar
  2. 2.
    Baader, F., Hladik, J., Peñaloza, R.: Automata can show PSPACE results for description logics. Inf. Comput. 206(9–10), 1045–1056 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Baader, F., Knechtel, M., Peñaloza, R.: Context-dependent views to axioms and consequences of semantic web ontologies. J. Web Semant. 12–13, 22–40 (2012)CrossRefGoogle Scholar
  4. 4.
    Baader, F., Peñaloza, R.: Automata-based axiom pinpointing. J. Autom. Reason. 45(2), 91–129 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Baader, F., Peñaloza, R.: Axiom pinpointing in general tableaux. J. Log. Comput. 20(1), 5–34 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Baader, F., Peñaloza, R., Suntisrivaraporn, B.: Pinpointing in the description logic \(\cal{EL}^+\). In: Hertzberg, J., Beetz, M., Englert, R. (eds.) KI 2007. LNCS (LNAI), vol. 4667, pp. 52–67. Springer, Heidelberg (2007). doi: 10.1007/978-3-540-74565-5_7 CrossRefGoogle Scholar
  7. 7.
    Belov, A., Lynce, I., Marques-Silva, J.: Towards efficient MUS extraction. AI Commun. 25(2), 97–116 (2012)MathSciNetzbMATHGoogle Scholar
  8. 8.
    Davis, M., Putnam, H.: A computing procedure for quantification theory. J. ACM 7(3), 201–215 (1960)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Dividino, R.Q., Schenk, S., Sizov, S., Staab, S.: Provenance, trust, explanations - and all that other meta knowledge. KI 23(2), 24–30 (2009)Google Scholar
  10. 10.
    Droste, M., Gastin, P.: Weighted automata and weighted logics. Theoret. Comput. Sci. 380(1–2), 69–86 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Gastin, P., Oddoux, D.: Fast LTL to Büchi automata translation. In: Berry, G., Comon, H., Finkel, A. (eds.) CAV 2001. LNCS, vol. 2102, pp. 53–65. Springer, Heidelberg (2001). doi: 10.1007/3-540-44585-4_6 CrossRefGoogle Scholar
  12. 12.
    Kalyanpur, A., Parsia, B., Horridge, M., Sirin, E.: Finding all justifications of OWL DL entailments. In: Aberer, K., et al. (eds.) ASWC/ISWC -2007. LNCS, vol. 4825, pp. 267–280. Springer, Heidelberg (2007). doi: 10.1007/978-3-540-76298-0_20 CrossRefGoogle Scholar
  13. 13.
    Kazakov, Y.: Consequence-driven reasoning for Horn SHIQ ontologies. In: Boutilier, C. (ed.) Proceedings of IJCAI 2009, pp. 2040–2045 (2009)Google Scholar
  14. 14.
    Kazakov, Y., Krötzsch, M., Simančík, F.: The incredible ELK: from polynomial procedures to efficient reasoning with \(\cal{E\!L}\) ontologies. J. Autom. Reason. 53, 1–61 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Kleine Büning, H., Kullmann, O.: Minimal unsatisfiability and autarkies. In: Handbook of Satisfiability, pp. 339–401 (2009)Google Scholar
  16. 16.
    Kullmann, O.: Investigations on autark assignments. Discret. Appl. Math. 107(1–3), 99–137 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Kullmann, O., Lynce, I., Marques-Silva, J.: Categorisation of clauses in conjunctive normal forms: minimally unsatisfiable sub-clause-sets and the lean kernel. In: Biere, A., Gomes, C.P. (eds.) SAT 2006. LNCS, vol. 4121, pp. 22–35. Springer, Heidelberg (2006). doi: 10.1007/11814948_4 CrossRefGoogle Scholar
  18. 18.
    Liffiton, M.H., Previti, A., Malik, A., Marques-Silva, J.: Fast, flexible MUS enumeration. Constraints 21(2), 223–250 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Nieuwenhuis, R., Oliveras, A.: Fast congruence closure and extensions. Inf. Comput. 205(4), 557–580 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Peñaloza, R.: Using sums-of-products for non-standard reasoning. In: Dediu, A.-H., Fernau, H., Martín-Vide, C. (eds.) LATA 2010. LNCS, vol. 6031, pp. 488–499. Springer, Heidelberg (2010). doi: 10.1007/978-3-642-13089-2_41 CrossRefGoogle Scholar
  21. 21.
    Riguzzi, F., Bellodi, E., Lamma, E., Zese, R.: Probabilistic description logics under the distribution semantics. Semant. Web 6(5), 477–501 (2015)CrossRefzbMATHGoogle Scholar
  22. 22.
    Schlobach, S., Cornet, R.: Non-standard reasoning services for the debugging of description logic terminologies. In: Proceedings of IJCAI 2003, pp. 355–362. Morgan Kaufmann (2003)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Technische Universität DresdenDresdenGermany
  2. 2.Free University of Bozen-BolzanoBolzanoItaly

Personalised recommendations