Skip to main content
SpringerLink
Log in

Semantics and Inference for Probabilistic Description Logics

  • Conference paper
  • First Online:
Uncertainty Reasoning for the Semantic Web III (URSW 2012, URSW 2011, URSW 2013)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8816))

Abstract

We present a semantics for Probabilistic Description Logics that is based on the distribution semantics for Probabilistic Logic Programming. The semantics, called DISPONTE, allows to express assertional probabilistic statements. We also present two systems for computing the probability of queries to probabilistic knowledge bases: BUNDLE and TRILL. BUNDLE is based on the Pellet reasoner while TRILL exploits the declarative Prolog language. Both algorithms compute a propositional Boolean formula that represents the set of explanations to the query. BUNDLE builds a formula in Disjunctive Normal Form in which each disjunct corresponds to an explanation while TRILL computes a general Boolean pinpointing formula using the techniques proposed by Baader and Peñaloza. Both algorithms then build a Binary Decision Diagram (BDD) representing the formula and compute the probability from the BDD using a dynamic programming algorithm. We also present experiments comparing the performance of BUNDLE and TRILL.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    http://javabdd.sourceforge.net/

  2. 2.

    http://sites.google.com/a/unife.it/ml/bundle/brca

  3. 3.

    http://cellontology.org/

  4. 4.

    http://ncit.nci.nih.gov/

  5. 5.

    http://phenoscape.org/wiki/Teleost_Anatomy_Ontology

  6. 6.

    http://dbpedia.org/

  7. 7.

    http://www.biopax.org/

  8. 8.

    http://www.vicodi.org/

References

  1. Baader, F., Calvanese, D., McGuinness, D.L., Nardi, D., Patel-Schneider, P.F. (eds.): The Description Logic Handbook: Theory, Implementation, and Applications. Cambridge University Press, Cambridge (2003)

    Google Scholar 

  2. Baader, F., Horrocks, I., Sattler, U.: Description logics. In: Handbook of Knowledge Representation, chap. 3, pp. 135–179. Elsevier, Amsterdam (2008)

    Google Scholar 

  3. Baader, F., Peñaloza, R.: Automata-based axiom pinpointing. J. Autom. Reasoning 45(2), 91–129 (2010)

    Article  MATH  Google Scholar 

  4. Baader, F., Peñaloza, R.: Axiom pinpointing in general tableaux. J. Log. Comput. 20(1), 5–34 (2010)

    Article  MATH  Google Scholar 

  5. Bacchus, F.: Representing and Reasoning with Probabilistic Knowledge - A Logical Approach to Probabilities. MIT Press, Cambridge (1990)

    Google Scholar 

  6. Beckert, B., Posegga, J.: leantap: Lean tableau-based deduction. J. Autom. Reasoning 15(3), 339–358 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  7. Bellodi, E., Lamma, E., Riguzzi, F., Albani, S.: A distribution semantics for probabilistic ontologies. In: International Workshop on Uncertainty Reasoning for the Semantic Web. CEUR Workshop Proceedings, vol. 778. Sun SITE Central Europe (2011)

    Google Scholar 

  8. Darwiche, A., Marquis, P.: A knowledge compilation map. J. Artif. Intell. Res. 17, 229–264 (2002)

    MATH  MathSciNet  Google Scholar 

  9. De Raedt, L., Kimmig, A., Toivonen, H.: ProbLog: a probabilistic Prolog and its application in link discovery. In: International Joint Conference on Artificial Intelligence, pp. 2462–2467 (2007)

    Google Scholar 

  10. Faizi, I.: A description logic prover in prolog, Bachelor’s thesis, Informatics Mathematical Modelling, Technical University of Denmark (2011)

    Google Scholar 

  11. Gomes, C.P., Sabharwal, A., Selman, B.: Model counting. In: Biere, A. (ed.) Handbook of Satisfiability. IOS Press, Amsterdam (2008)

    Google Scholar 

  12. Haarslev, V., Hidde, K., Möller, R., Wessel, M.: The racerpro knowledge representation and reasoning system. Semant. Web 3(3), 267–277 (2012)

    Google Scholar 

  13. Halaschek-Wiener, C., Kalyanpur, A., Parsia, B.: Extending tableau tracing for ABox updates. Technical report, University of Maryland (2006)

    Google Scholar 

  14. Halpern, J.Y.: An analysis of first-order logics of probability. Artif. Intell. 46(3), 311–350 (1990)

    Article  MATH  Google Scholar 

  15. Herchenröder, T.: Lightweight semantic web oriented reasoning in prolog: tableaux inference for description logics. Master’s thesis, School of Informatics, University of Edinburgh (2006)

    Google Scholar 

  16. Hitzler, P., Krötzsch, M., Rudolph, S.: Foundations of Semantic Web Technologies. CRC Press, Boca Raton (2009)

    Google Scholar 

  17. Hustadt, U., Motik, B., Sattler, U.: Deciding expressive description logics in the framework of resolution. Inf. Comput. 206(5), 579–601 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  18. Kalyanpur, A.: Debugging and repair of OWL ontologies. Ph.D. thesis, The Graduate School of the University of Maryland (2006)

    Google Scholar 

  19. Kalyanpur, A., Parsia, B., Horridge, M., Sirin, E.: Finding all justifications of OWL DL entailments. In: Aberer, K., et al. (eds.) ISWC/ASWC 2007. LNCS, vol. 4825, pp. 267–280. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  20. Kalyanpur, A., Parsia, B., Sirin, E., Hendler, J.A.: Debugging unsatisfiable classes in OWL ontologies. J. Web Sem. 3(4), 268–293 (2005)

    Article  Google Scholar 

  21. Klinov, P.: Pronto: a non-monotonic probabilistic description logic reasoner. In: Bechhofer, S., Hauswirth, M., Hoffmann, J., Koubarakis, M. (eds.) ESWC 2008. LNCS, vol. 5021, pp. 822–826. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  22. Klinov, P., Parsia, B.: Optimization and evaluation of reasoning in probabilistic description logic: towards a systematic approach. In: Sheth, A.P., Staab, S., Dean, M., Paolucci, M., Maynard, D., Finin, T., Thirunarayan, K. (eds.) ISWC 2008. LNCS, vol. 5318, pp. 213–228. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  23. Klinov, P., Parsia, B.: A hybrid method for probabilistic satisfiability. In: Bjørner, N., Sofronie-Stokkermans, V. (eds.) CADE 2011. LNCS, vol. 6803, pp. 354–368. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  24. Lukácsy, G., Szeredi, P.: Efficient description logic reasoning in prolog: the dlog system. TPLP 9(3), 343–414 (2009)

    MATH  Google Scholar 

  25. Lukasiewicz, T.: Expressive probabilistic description logics. Artif. Int. 172(6–7), 852–883 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  26. Meissner, A.: An automated deduction system for description logic with alcn language. Studia z Automatyki i Informatyki 28–29, 91–110 (2004)

    Google Scholar 

  27. Nilsson, N.J.: Probabilistic logic. Artif. Intell. 28(1), 71–87 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  28. Patel-Schneider, P.F., Horrocks, I., Bechhofer, S.: Tutorial on OWL (2003)

    Google Scholar 

  29. Poole, D.: The Independent Choice Logic for modelling multiple agents under uncertainty. Artif. Intell. 94(1–2), 7–56 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  30. Poole, D.: Probabilistic horn abduction and Bayesian networks. Artif. Intell. 64(1), 81–129 (1993)

    Article  MATH  Google Scholar 

  31. Reiter, R.: A theory of diagnosis from first principles. Artif. Intell. 32(1), 57–95 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  32. Ricca, F., Gallucci, L., Schindlauer, R., Dell’Armi, T., Grasso, G., Leone, N.: Ontodlv: an asp-based system for enterprise ontologies. J. Log. Comput. 19(4), 643–670 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  33. Riguzzi, F.: Extended semantics and inference for the Independent Choice Logic. Log. J. IGPL 17(6), 589–629 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  34. Riguzzi, F., Bellodi, E., Lamma, E.: Probabilistic Datalog+/- under the distribution semantics. In: Kazakov, Y., Lembo, D., Wolter, F. (eds.) International Workshop on Description Logics (2012)

    Google Scholar 

  35. Riguzzi, F., Bellodi, E., Lamma, E., Zese, R.: Computing instantiated explanations in OWL DL. In: Baldoni, M., Baroglio, C., Boella, G., Micalizio, R. (eds.) AI*IA 2013. LNCS, vol. 8249, pp. 397–408. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  36. Riguzzi, F., Bellodi, E., Lamma, E., Zese, R.: Probabilistic description logics under the distribution semantics. Semant. Web J. (to appear, 2014)

    Google Scholar 

  37. Riguzzi, F., Lamma, E., Bellodi, E., Zese, R.: Epistemic and statistical probabilistic ontologies. In: Uncertainty Reasoning for the Semantic Web. CEUR Workshop Proceedings, vol. 900, pp. 3–14. Sun SITE Central Europe (2012)

    Google Scholar 

  38. Sang, T., Beame, P., Kautz, H.A.: Performing bayesian inference by weighted model counting. In: Proceedings of AAAI, pp. 475–482. AAAI Press/The MIT Press, Palo Alto, Pittsburgh, 9–13 July 2005

    Google Scholar 

  39. Sato, T.: A statistical learning method for logic programs with distribution semantics. In: International Conference on Logic Programming, pp. 715–729. MIT Press (1995)

    Google Scholar 

  40. Sato, T., Kameya, Y.: Parameter learning of logic programs for symbolic-statistical modeling. J. Artif. Intell. Res. 15, 391–454 (2001)

    MATH  MathSciNet  Google Scholar 

  41. Schlobach, S., Cornet, R.: Non-standard reasoning services for the debugging of description logic terminologies. In: International Joint Conference on Artificial Intelligence, pp. 355–362. Morgan Kaufmann (2003)

    Google Scholar 

  42. Schmidt-Schauß, M., Smolka, G.: Attributive concept descriptions with complements. Artif. Intell. 48(1), 1–26 (1991)

    Article  MATH  Google Scholar 

  43. Shearer, R., Motik, B., Horrocks, I.: Hermit: A highly-efficient owl reasoner. In: OWLED (2008)

    Google Scholar 

  44. Sirin, E., Parsia, B., Cuenca-Grau, B., Kalyanpur, A., Katz, Y.: Pellet: a practical OWL-DL reasoner. J. Web Sem. 5(2), 51–53 (2007)

    Article  Google Scholar 

  45. Vassiliadis, V., Wielemaker, J., Mungall, C.: Processing owl2 ontologies using thea: an application of logic programming. In: International Workshop on OWL: Experiences and Directions. CEUR Workshop Proceedings, vol. 529. CEUR-WS.org (2009)

    Google Scholar 

  46. Vennekens, J., Denecker, M., Bruynooghe, M.: CP-logic: a language of causal probabilistic events and its relation to logic programming. Theory Pract. Log. Program. 9(3), 245–308 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  47. Vennekens, J., Verbaeten, S., Bruynooghe, M.: Logic programs with annotated disjunctions. In: Demoen, B., Lifschitz, V. (eds.) ICLP 2004. LNCS, vol. 3132, pp. 431–445. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Ingegneria, University of Ferrara, Ferrara, Italy

    Riccardo Zese, Elena Bellodi, Evelina Lamma & Fabiano Aguiari

  2. Dipartimento di Matematica e Informatica, University of Ferrara, Via Saragat 1, 44122, Ferrara, Italy

    Fabrizio Riguzzi

Authors
  1. Riccardo Zese
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Elena Bellodi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Evelina Lamma
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Fabrizio Riguzzi
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Fabiano Aguiari
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Fabrizio Riguzzi .

Editor information

Editors and Affiliations

  1. University of Zaragoza, Zaragoza, Spain

    Fernando Bobillo

  2. Universidade de Brasília, Brasília, Brazil

    Rommel N. Carvalho

  3. George Mason University, Fairfax, Virginia, USA

    Paulo C.G. Costa

  4. Università degli Studi di Bari, Bari, Italy

    Claudia d'Amato

  5. Università degli Studi di Bari, Bari, Italy

    Nicola Fanizzi

  6. George Mason University, Fairfax, Virginia, USA

    Kathryn B. Laskey

  7. MITRE Corporation, McLean, Virginia, USA

    Kenneth J. Laskey

  8. University of Oxford, Oxford, United Kingdom

    Thomas Lukasiewicz

  9. National University of Ireland, Galway, Ireland

    Matthias Nickles

  10. Goldman Sachs, Washington, District of Columbia, USA

    Michael Pool

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Zese, R., Bellodi, E., Lamma, E., Riguzzi, F., Aguiari, F. (2014). Semantics and Inference for Probabilistic Description Logics. In: Bobillo, F., et al. Uncertainty Reasoning for the Semantic Web III. URSW URSW URSW 2012 2011 2013. Lecture Notes in Computer Science(), vol 8816. Springer, Cham. https://doi.org/10.1007/978-3-319-13413-0_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-13413-0_5

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-13412-3

  • Online ISBN: 978-3-319-13413-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation