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Ontology-Mediated Probabilistic Model Checking

  • Clemens DubslaffEmail author
  • Patrick Koopmann
  • Anni-Yasmin Turhan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11918)

Abstract

Probabilistic model checking (PMC) is a well-established method for the quantitative analysis of dynamic systems. Description logics (DLs) provide a well-suited formalism to describe and reason about terminological knowledge, used in many areas to specify background knowledge on the domain. We investigate how such knowledge can be integrated into the PMC process, introducing ontology-mediated PMC. Specifically, we propose a formalism that links ontologies to dynamic behaviors specified by guarded commands, the de-facto standard input formalism for PMC tools such as Prism. Further, we present and implement a technique for their analysis relying on existing DL-reasoning and PMC tools. This way, we enable the application of standard PMC techniques to analyze knowledge-intensive systems. Our approach is implemented and evaluated on a multi-server system case study, where different DL-ontologies are used to provide specifications of different server platforms and situations the system is executed in.

References

  1. 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)zbMATHGoogle Scholar
  2. 2.
    Baader, F., Hanschke, P.: A scheme for integrating concrete domains into concept languages. In: Proceedings of IJCAI 1991, pp. 452–457. Morgan Kaufmann (1991)Google Scholar
  3. 3.
    Baader, F., Horrocks, I., Lutz, C., Sattler, U.: An Introduction to Description Logic. Cambridge University Press, Cambridge (2017)CrossRefGoogle Scholar
  4. 4.
    Baader, F., Zarrieß, B.: Verification of Golog programs over description logic actions. In: Fontaine, P., Ringeissen, C., Schmidt, R.A. (eds.) FroCoS 2013. LNCS (LNAI), vol. 8152, pp. 181–196. Springer, Heidelberg (2013).  https://doi.org/10.1007/978-3-642-40885-4_12CrossRefzbMATHGoogle Scholar
  5. 5.
    Baier, C., Daum, M., Dubslaff, C., Klein, J., Klüppelholz, S.: Energy-utility quantiles. In: Badger, J.M., Rozier, K.Y. (eds.) NFM 2014. LNCS, vol. 8430, pp. 285–299. Springer, Cham (2014).  https://doi.org/10.1007/978-3-319-06200-6_24CrossRefGoogle Scholar
  6. 6.
    Baier, C., Katoen, J.P.: Principles of Model Checking. MIT Press, Cambridge (2008)zbMATHGoogle Scholar
  7. 7.
    Baier, C., Chrszon, P., Dubslaff, C., Klein, J., Klüppelholz, S.: Energy-utility analysis of probabilistic systems with exogenous coordination. In: de Boer, F., Bonsangue, M., Rutten, J. (eds.) It’s All About Coordination. LNCS, vol. 10865, pp. 38–56. Springer, Cham (2018).  https://doi.org/10.1007/978-3-319-90089-6_3CrossRefGoogle Scholar
  8. 8.
    Baier, C., et al.: Probabilistic model checking and non-standard multi-objective reasoning. In: Gnesi, S., Rensink, A. (eds.) FASE 2014. LNCS, vol. 8411, pp. 1–16. Springer, Heidelberg (2014).  https://doi.org/10.1007/978-3-642-54804-8_1CrossRefGoogle Scholar
  9. 9.
    Bienvenu, M., Ortiz, M.: Ontology-mediated query answering with data-tractable description logics. In: Reasoning Web, Web Logic Rules, pp. 218–307 (2015)CrossRefGoogle Scholar
  10. 10.
    Calvanese, D., De Giacomo, G., Lembo, D., Lenzerini, M., Rosati, R.: Tractable reasoning and efficient query answering in description logics: the DL-lite family. J. Autom. Reasoning 39(3), 385–429 (2007)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Calvanese, D., De Giacomo, G., Lenzerini, M., Rosati, R.: Actions and programs over description logic knowledge bases: a functional approach. In: Knowing, Reasoning, and Acting: Essays in Honour of H. J. Levesque, College Publications (2011)Google Scholar
  12. 12.
    Chrszon, P., Dubslaff, C., Klüppelholz, S., Baier, C.: Family-based modeling and analysis for probabilistic systems – featuring ProFeat. In: Stevens, P., Wąsowski, A. (eds.) FASE 2016. LNCS, vol. 9633, pp. 287–304. Springer, Heidelberg (2016).  https://doi.org/10.1007/978-3-662-49665-7_17CrossRefGoogle Scholar
  13. 13.
    Dhaussy, P., Boniol, F., Roger, J.C., Leroux, L.: Improving model checking with context modelling. Adv. Softw. Eng. 2012, 13 (2012)CrossRefGoogle Scholar
  14. 14.
    Dijkstra, E.W.: A Discipline of Programming. Prentice-Hall, Upper Saddle River (1976)zbMATHGoogle Scholar
  15. 15.
    Dubslaff, C., Baier, C., Klüppelholz, S.: Probabilistic model checking for feature-oriented systems. Trans. Aspect Oriented Softw. Dev. 12, 180–220 (2015)Google Scholar
  16. 16.
    Dubslaff, C., Koopmann, P., Turhan, A.Y.: Ontology-mediated probabilistic model checking (extended version). LTCS-Report 19–05, TU Dresden, Dresden, Germany (2019). https://lat.inf.tu-dresden.de/research/reports.html
  17. 17.
    Forejt, V., Kwiatkowska, M., Norman, G., Parker, D.: Automated verification techniques for probabilistic systems. In: Bernardo, M., Issarny, V. (eds.) SFM 2011. LNCS, vol. 6659, pp. 53–113. Springer, Heidelberg (2011).  https://doi.org/10.1007/978-3-642-21455-4_3CrossRefGoogle Scholar
  18. 18.
    Hariri, B.B., Calvanese, D., Montali, M., De Giacomo, G., De Masellis, R., Felli, P.: Description logic knowledge and action bases. J. Artif. Intell. Res. 46, 651–686 (2013)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Horridge, M., Bechhofer, S.: The OWL API: a Java API for OWL ontologies. Semant. Web 2(1), 11–21 (2011)Google Scholar
  20. 20.
    Horrocks, I., Kutz, O., Sattler, U.: The even more irresistible \(\cal{SROIQ}\). In: Proceedings of KR 2006, pp. 57–67. AAAI Press (2006)Google Scholar
  21. 21.
    Jifeng, H., Seidel, K., McIver, A.: Probabilistic models for the guarded command language. Sci. Comput. Program. 28(2), 171–192 (1997)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Kazakov, Y.: \(\cal{RIQ}\) and \(\cal{SROIQ}\) are harder than \(\cal{SHOIQ}\). In: Proceedings of the 11th International Conference on Principles of Knowledge Representation and Reasoning (KR 2008), pp. 274–284. AAAI Press (2008)Google Scholar
  23. 23.
    Klein, J., et al.: Advances in probabilistic model checking with PRISM: variable reordering, quantiles and weak deterministic büchi automata. Int. J. Softw. Tools Technol. Transfer 20(2), 179–194 (2018)CrossRefGoogle Scholar
  24. 24.
    Kwiatkowska, M., Norman, G., Parker, D.: PRISM 4.0: verification of probabilistic real-time systems. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 585–591. Springer, Heidelberg (2011).  https://doi.org/10.1007/978-3-642-22110-1_47CrossRefGoogle Scholar
  25. 25.
    Lutz, C.: Inverse roles make conjunctive queries hard. In: Proceedings of the 20th International Workshop on Description Logics (DL 2007), CEUR Workshop Proceedings, vol. 250 (2007). CEUR-WS.org
  26. 26.
    Mauro, J., Nieke, M., Seidl, C., Yu, I.C.: Context aware reconfiguration in software product lines. In: Proceedings of the 10th International Workshop on Variability Modelling of Software-Intensive Systems (VaMoS 2016), pp. 41–48. ACM (2016)Google Scholar
  27. 27.
    Miner, A., Parker, D.: Symbolic representations and analysis of large probabilistic systems. In: Baier, C., Haverkort, B.R., Hermanns, H., Katoen, J.-P., Siegle, M. (eds.) Validation of Stochastic Systems. LNCS, vol. 2925, pp. 296–338. Springer, Heidelberg (2004).  https://doi.org/10.1007/978-3-540-24611-4_9CrossRefzbMATHGoogle Scholar
  28. 28.
    Motik, B., Cuenca Grau, B., Horrocks, I., Wu, Z., Fokoue, A., Lutz, C.: OWL 2 web ontology language profiles. W3C Recommendation, 27 October 2009. http://www.w3.org/TR/2009/REC-owl2-profiles-20091027/
  29. 29.
    Ngo, N., Ortiz, M., Simkus, M.: Closed predicates in description logics: results on combined complexity. In: Proceedings of KR 2016, pp. 237–246. AAAI Press (2016)Google Scholar
  30. 30.
    Parsia, B., Matentzoglu, N., Gonçalves, R.S., Glimm, B., Steigmiller, A.: The OWL reasoner evaluation (ORE) 2015 competition report. J. Autom. Reasoning 59(4), 455–482 (2017)MathSciNetCrossRefGoogle Scholar
  31. 31.
    Poggi, A., Lembo, D., Calvanese, D., De Giacomo, G., Lenzerini, M., Rosati, R.: Linking data to ontologies. J. Data Semant. 4900, 133–173 (2008)zbMATHGoogle Scholar
  32. 32.
    Puterman, M.: Markov Decision Processes: Discrete Stochastic Dynamic Programming. Wiley, New York (1994)CrossRefGoogle Scholar
  33. 33.
    Rudolph, S., Glimm, B.: Nominals, inverses, counting, and conjunctive queries or: why infinity is your friend!. J. Artif. Intell. Res. 39, 429–481 (2010)MathSciNetCrossRefGoogle Scholar
  34. 34.
    Sirin, E., Parsia, B., Grau, B.C., Kalyanpur, A., Katz, Y.: Pellet: a practical OWL-DL reasoner. J. Web Semant. 5(2), 51–53 (2007)CrossRefGoogle Scholar
  35. 35.
    Tobies, S.: Complexity results and practical algorithms for logics in knowledge representation. Ph.D. thesis, RWTH Aachen University, Germany (2001)Google Scholar
  36. 36.
    Zarrieß, B., Claßen, J.: Verification of knowledge-based programs over description logic actions. In: IJCAI, pp. 3278–3284. AAAI Press (2015)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Technische Universität DresdenDresdenGermany

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