Capturing Graded Knowledge and Uncertainty in a Modalized Fragment of OWL

Hans-Ulrich Krieger

Abstract

Natural language statements uttered in diagnosis (e.g., in medicine), but more general in daily life are usually graded, i.e., are associated with a degree of uncertainty about the validity of an assessment and is often expressed through specific verbs, adverbs, or adjectives in natural language. In this paper, we look into a representation of such graded statements by presenting a simple non-standard modal logic which comes with a set of modal operators, directly associated with the words indicating the uncertainty and interpreted through confidence intervals in the model theory. We complement the model theory by a set of RDFS-/OWL 2 RL-like entailment (if-then) rules, acting on the syntactic representation of modalized statements. Our interest in such a formalization is related to the use of OWL as the de facto language in today’s ontologies and its weakness to represent and reason about assertional knowledge that is uncertain or that changes over time.

References

  1. Areces, C., Hoffmann, G., and Denis, A. (2010). Modal logics with counting. In Proceedings of the 17th Workshop on Logic, Language, Information and Computation (WoLLIC), pages 98-109.
  2. Bishop, B., Kiryakov, A., Ognyanoff, D., Peikov, I., Tashev, Z., and Velkov, R. (2011). OWLIM: A family of scalable semantic repositories. Semantic Web, 2(1):33-42.
  3. Blackburn, P., de Rijke, M., and Venema, Y. (2001). Modal Logic. Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, Cambridge.
  4. Carroll, J. J., Dickinson, I., Dollin, C., Reynolds, D., Seaborne, A., and Wilkinson, K. (2004). Jena: Implementing the Semantic Web recommendations. In Proceedings of the 13th international World Wide Web conference (WWW), pages 74-83.
  5. Devlin, K. (2006). Situation theory and situation semantics. In Gabbay, D. M. and Woods, J., editors, Handbook of the History of Logic. Volume 7, pages 601-664. Elsevier.
  6. Dubois, D. and Prade, H. (1994). Can we enforce full compositionality in uncertainty calculi. In Proceedings of the 12th National Conference on Artificial Intelligence, pages 149-154.
  7. Fine, K. (1972). In so many possible worlds. Notre Dame Journal of Formal Logic, 13(4):516-520.
  8. Golbreich, C. and Wallace, E. K. (2012). OWL 2 web ontology language new features and rationale (second edition). Technical report, W3C.
  9. Halpern, J. Y. (1990). An analysis of first-order logics of probability. Artificial Intelligence, 46:311-350.
  10. Halpern, J. Y. (2003). Reasoning About Uncertainty. MIT Press, Cambridge, MA.
  11. Hayes, P. (2004). RDF semantics. Technical report, W3C.
  12. Heinsohn, J. (1993). ALCP - Ein hybrider Ansatz zur Modellierung von Unsicherheit in terminologischen Logiken. PhD thesis, Universität des Saarlandes. In German.
  13. Jaeger, M. (1994). Probabilistic reasoning in terminological logics. In Proceedings of the 4th International Conference on Principles of Knowledge Representation and Reasoning (KR), pages 305-316.
  14. Jøsang, A. (1997). Artificial reasoning with subjective logic. In Proceedings of the 2nd Australian Workshop on Commonsense Reasoning.
  15. Jøsang, A. (2001). A logic for uncertain probabilities. International Journal of Uncertainty, Fuzzyness and Knowledge-Based Systems, 9(3):279-311.
  16. Koller, D. and Friedmann, N. (2009). Probabilistic Graphical Models. MIT Press.
  17. Krengel, U. (2003). Einführung in die Wahrscheinlichkeitstheorie und Statistik. Vieweg, 7th edition. In German.
  18. Krieger, H.-U. (2012). A temporal extension of the Hayes/ter Horst entailment rules and an alternative to W3C's n-ary relations. In Proceedings of the 7th International Conference on Formal Ontology in Information Systems (FOIS), pages 323-336.
  19. Krieger, H.-U. (2013). An efficient implementation of equivalence relations in OWL via rule and query rewriting. In Proceedings of the 7th IEEE International Conference on Semantic Computing (ICSC), pages 260-263.
  20. Lucas, P. J., van der Gaag, L. C., and Abu-Hanna, A. (2004). Bayesian networks in biomedicine and health-care. Artificial Intelligence in Medicine, 30:201-214.
  21. Motik, B., Cuenca Grau, B., Horrocks, I., Wu, Z., Fokoue, A., and Lutz, C. (2012). OWL 2 web ontology language profiles. Technical report, W3C. W3C Recommendation 11 December 2012.
  22. Pearl, J. (1988). Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann, San Francisco, CA, MA.
  23. Richardson, M. and Domingos, P. (2006). Markov logic networks. Machine Learning, 62(1-2):107-136.
  24. Schulz, S., Martínez-Costa, C., Karlsson, D., Cornet, R., Brochhausen, M., and Rector, A. (2014). An ontological analysis of reference in health record statements. In Proceedings of the 8th International Conference on Formal Ontology in Information Systems (FOIS 2014).
  25. Stoilos, G., Stamou, G. B., Tzouvaras, V., Pan, J. Z., and Horrocks, I. (2005). Fuzzy OWL: uncertainty and the semantic web. In Proceedings of the OWLED 7805 Workshop on OWL: Experiences and Directions.
  26. Straccia, U. (2001). Reasoning within fuzzy description logics. Journal of Artificial Intelligence Research, 14:147-176.
  27. ter Horst, H. J. (2005). Completeness, decidability and complexity of entailment for RDF Schema and a semantic extension involving the OWL vocabulary. Journal of Web Semantics, 3:79-115.
  28. Tresp, C. B. and Molitor, R. (1998). A description logic for vague knowledge. In Proceedings of the 13th European Conference on Artificial Intelligence (ECAI), pages 361-365.
  29. Wikipedia (2015). Modal logic - Wikipedia, The Free Encyclopedia. [Online; accessed 19-June-2015].
  30. Wilson, N. (2000). Algorithms for Dempster-Shafer theory. In Algorithms for Uncertainty and Defeasible Reasoning, Handbook of Defeasible Reasoning and Uncertainty Management Systems, pages 421-475. Kluwer.
Download


Paper Citation


in Harvard Style

Krieger H. (2016). Capturing Graded Knowledge and Uncertainty in a Modalized Fragment of OWL . In Proceedings of the 8th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART, ISBN 978-989-758-172-4, pages 19-30. DOI: 10.5220/0005628100190030


in Bibtex Style

@conference{icaart16,
author={Hans-Ulrich Krieger},
title={Capturing Graded Knowledge and Uncertainty in a Modalized Fragment of OWL},
booktitle={Proceedings of the 8th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,},
year={2016},
pages={19-30},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005628100190030},
isbn={978-989-758-172-4},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 8th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,
TI - Capturing Graded Knowledge and Uncertainty in a Modalized Fragment of OWL
SN - 978-989-758-172-4
AU - Krieger H.
PY - 2016
SP - 19
EP - 30
DO - 10.5220/0005628100190030