BEACON: An Efficient SAT-Based Tool for Debugging \({\mathcal {EL}}{^+}\) Ontologies

  • M. Fareed Arif
  • Carlos MencíaEmail author
  • Alexey Ignatiev
  • Norbert Manthey
  • Rafael Peñaloza
  • Joao Marques-Silva
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9710)


Description Logics (DLs) are knowledge representation and reasoning formalisms used in many settings. Among them, the \({\mathcal {EL}}\) family of DLs stands out due to the availability of polynomial-time inference algorithms and its ability to represent knowledge from domains such as medical informatics. However, the construction of an ontology is an error-prone process which often leads to unintended inferences. This paper presents the BEACON tool for debugging \({\mathcal {EL}{^+}}\) ontologies. BEACON builds on earlier work relating minimal justifications (MinAs) of \({\mathcal {EL}{^+}}\) ontologies and MUSes of a Horn formula, and integrates state-of-the-art algorithms for solving different function problems in the SAT domain.


Description Logic Horn Clause Unit Clause Horn Formula Subsumption Relation 
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.



This work was funded in part by SFI grant BEACON (09/IN.1/I2618), by DFG grant DFG HO 1294/11-1, and by Spanish grant TIN2013-46511-C2-2-P. The contribution of the researchers associated with the SFI grant BEACON is also acknowledged.


  1. 1.
    Arif, M.F., Mencía, C., Marques-Silva, J.: Efficient axiom pinpointing with EL2MCS. In: Hölldobler, S., Krötzsch, M., Peñaloza, R., Rudolph, S., Edelkamp, S., Edelkamp, S. (eds.) KI 2015. LNCS, vol. 9324, pp. 225–233. Springer, Heidelberg (2015). doi: 10.1007/978-3-319-24489-1_17 CrossRefGoogle Scholar
  2. 2.
    Arif, M.F., Mencía, C., Marques-Silva, J.: Efficient MUS enumeration of Horn formulae with applications to axiom pinpointing. In: Heule, M., Weaver, S. (eds.) SAT 2015. LNCS, vol. 9340, pp. 324–342. Springer, Heidelberg (2015). doi: 10.1007/978-3-319-24318-4_24 CrossRefGoogle Scholar
  3. 3.
    Ashburner, M., Ball, C.A., Blake, J.A., Botstein, D., Butler, H., Cherry, J.M., Davis, A.P., Dolinski, K., Dwight, S.S., Eppig, J.T., et al.: Gene ontology: tool for the unification of biology. Nat. Genet. 25(1), 25–29 (2000)CrossRefGoogle Scholar
  4. 4.
    Baader, F., Brandt, S., Lutz, C.: Pushing the \({\cal EL}\) envelope. In: IJCAI, pp. 364–369 (2005)Google Scholar
  5. 5.
    Baader, F., Lutz, C., Suntisrivaraporn, B.: \(\sf {CEL}\) — a polynomial-time reasoner for life science ontologies. In: Furbach, U., Shankar, N. (eds.) IJCAR 2006. LNCS (LNAI), vol. 4130, pp. 287–291. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  6. 6.
    Baader, F., Peñaloza, R., Suntisrivaraporn, B.: Pinpointing in the description logic \({\cal EL{^+}}\) . In: KI, pp. 52–67 (2007)Google Scholar
  7. 7.
    Baader, F., Suntisrivaraporn, B.: Debugging SNOMED CT using axiom pinpointing in the description logic \({\cal EL{^+}}\) . In: KR-MED (2008)Google Scholar
  8. 8.
    Bailey, J., Stuckey, P.J.: Discovery of minimal unsatisfiable subsets of constraints using hitting set dualization. In: Hermenegildo, M.V., Cabeza, D. (eds.) PADL 2004. LNCS, vol. 3350, pp. 174–186. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  9. 9.
    Biere, A., Heule, M., van Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. Frontiers in Artificial Intelligence and Applications, vol. 185. IOS Press, Amsterdam (2009)zbMATHGoogle Scholar
  10. 10.
    Birnbaum, E., Lozinskii, E.L.: Consistent subsets of inconsistent systems: structure and behaviour. J. Exp. Theor. Artif. Intell. 15(1), 25–46 (2003)CrossRefzbMATHGoogle Scholar
  11. 11.
    Davies, J., Bacchus, F.: Solving MAXSAT by solving a sequence of simpler SAT instances. In: Lee, J. (ed.) CP 2011. LNCS, vol. 6876, pp. 225–239. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  12. 12.
    Dowling, W.F., Gallier, J.H.: Linear-time algorithms for testing the satisfiability of propositional Horn formulae. J. Log. Program. 1(3), 267–284 (1984)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Gupta, A.: Learning Abstractions for Model Checking. Ph.D. thesis, Carnegie Mellon University, June 2006Google Scholar
  14. 14.
    Ignatiev, A., Previti, A., Liffiton, M., Marques-Silva, J.: Smallest MUS extraction with minimal hitting set dualization. In: Pesant, G. (ed.) CP 2015. LNCS, vol. 9255, pp. 173–182. Springer, Heidelberg (2015)Google Scholar
  15. 15.
    Itai, A., Makowsky, J.A.: Unification as a complexity measure for logic programming. J. Log. Program. 4(2), 105–117 (1987)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Liberatore, P.: Redundancy in logic I: CNF propositional formulae. Artif. Intell. 163(2), 203–232 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Liffiton, M.H., Malik, A.: Enumerating infeasibility: finding multiple MUSes quickly. In: Gomes, C., Sellmann, M. (eds.) CPAIOR 2013. LNCS, vol. 7874, pp. 160–175. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  18. 18.
    Liffiton, M.H., Previti, A., Malik, A., Marques-Silva, J.: Fast, flexible MUs enumeration. Constraints (2015). Online version:
  19. 19.
    Liffiton, M.H., Sakallah, K.A.: Algorithms for computing minimal unsatisfiable subsets of constraints. J. Autom. Reasoning 40(1), 1–33 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Ludwig, M.: Just: a tool for computing justifications w.r.t. ELH ontologies. In: ORE (2014)Google Scholar
  21. 21.
    Manthey, N., Peñaloza, R.: Exploiting SAT technology for axiom pinpointing. Technical report LTCS 15–05, Chair of Automata Theory, Institute of Theoretical Computer Science, Technische Universität Dresden, April 2015.
  22. 22.
    Marques-Silva, J., Heras, F., Janota, M., Previti, A., Belov, A.: On computing minimal correction subsets. In: IJCAI, pp. 615–622 (2013)Google Scholar
  23. 23.
    Mencía, C., Previti, A., Marques-Silva, J.: Literal-based MCS extraction. In: IJCAI, pp. 1973–1979 (2015)Google Scholar
  24. 24.
    Minoux, M.: LTUR: A simplified linear-time unit resolution algorithm for Horn formulae and computer implementation. Inf. Process. Lett. 29(1), 1–12 (1988)MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Peñaoza, R.: Axiom pinpointing in description logics and beyond. Ph.D. thesis, Dresden University of Technology (2009)Google Scholar
  26. 26.
    Previti, A., Marques-Silva, J.: Partial MUS enumeration. In: AAAI, pp. 818–825 (2013)Google Scholar
  27. 27.
    Rector, A.L., Horrocks, I.R.: Experience building a large, re-usable medical ontology using a description logic with transitivity and concept inclusions. In: Workshop on Ontological Engineering, pp. 414–418 (1997)Google Scholar
  28. 28.
    Reiter, R.: A theory of diagnosis from first principles. Artif. Intell. 32(1), 57–95 (1987)MathSciNetCrossRefzbMATHGoogle Scholar
  29. 29.
    Schlobach, S., Cornet, R.: Non-standard reasoning services for the debugging of description logic terminologies. In: IJCAI, pp. 355–362 (2003)Google Scholar
  30. 30.
    Sebastiani, R., Vescovi, M.: Axiom pinpointing in lightweight description logics via Horn-SAT encoding and conflict analysis. In: Schmidt, R.A. (ed.) CADE-22. LNCS, vol. 5663, pp. 84–99. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  31. 31.
    Sebastiani, R., Vescovi, M.: Axiom pinpointing in large \({\cal EL{^+}}\) ontologies via SAT and SMT techniques. Technical report DISI-15-010, DISI, University of Trento, Italy, Under Journal Submission, April 2015.
  32. 32.
    Sioutos, N., de Coronado, S., Haber, M.W., Hartel, F.W., Shaiu, W., Wright, L.W.: NCI thesaurus: A semantic model integrating cancer-related clinical and molecular information. J. Biomed. Inform. 40(1), 30–43 (2007)CrossRefGoogle Scholar
  33. 33.
    Slaney, J.: Set-theoretic duality: A fundamental feature of combinatorial optimisation. In: ECAI, pp. 843–848 (2014)Google Scholar
  34. 34.
    Spackman, K.A., Campbell, K.E., Côté, R.A.: SNOMED RT: a reference terminology for health care. In: AMIA (1997)Google Scholar
  35. 35.
    Stefan, S., Ronald, C., Spackman, K.A.: Consolidating SNOMED CT’s ontological commitment. Appl. Ontol. 6, 111 (2011)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • M. Fareed Arif
    • 1
  • Carlos Mencía
    • 2
    Email author
  • Alexey Ignatiev
    • 3
    • 6
  • Norbert Manthey
    • 4
  • Rafael Peñaloza
    • 5
  • Joao Marques-Silva
    • 3
  1. 1.University College DublinDublinIreland
  2. 2.University of OviedoOviedoSpain
  3. 3.University of LisbonLisbonPortugal
  4. 4.TU DresdenDresdenGermany
  5. 5.Free University of Bozen-BolzanoBolzanoItaly
  6. 6.ISDCT SB RASIrkutskRussia

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