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.
The authors are supported by the DFG through the Collaborative Research Centers CRC 912 (HAEC) and TRR 248 (see https://perspicuous-computing.science, project ID 389792660), the Cluster of Excellence EXC 2050/1 (CeTI, project ID 390696704, as part of Germany’s Excellence Strategy), and the Research Training Groups QuantLA (GRK 1763) and RoSI (GRK 1907).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Notes
- 1.
Hardware setup: Intel Xeon E5-2680@2.70 GHz, 128 GB RAM; Turbo Boost and HT enabled; Debian GNU/Linux 9.1.
References
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)
Baader, F., Hanschke, P.: A scheme for integrating concrete domains into concept languages. In: Proceedings of IJCAI 1991, pp. 452–457. Morgan Kaufmann (1991)
Baader, F., Horrocks, I., Lutz, C., Sattler, U.: An Introduction to Description Logic. Cambridge University Press, Cambridge (2017)
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_12
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_24
Baier, C., Katoen, J.P.: Principles of Model Checking. MIT Press, Cambridge (2008)
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_3
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_1
Bienvenu, M., Ortiz, M.: Ontology-mediated query answering with data-tractable description logics. In: Reasoning Web, Web Logic Rules, pp. 218–307 (2015)
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)
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)
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_17
Dhaussy, P., Boniol, F., Roger, J.C., Leroux, L.: Improving model checking with context modelling. Adv. Softw. Eng. 2012, 13 (2012)
Dijkstra, E.W.: A Discipline of Programming. Prentice-Hall, Upper Saddle River (1976)
Dubslaff, C., Baier, C., Klüppelholz, S.: Probabilistic model checking for feature-oriented systems. Trans. Aspect Oriented Softw. Dev. 12, 180–220 (2015)
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
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_3
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)
Horridge, M., Bechhofer, S.: The OWL API: a Java API for OWL ontologies. Semant. Web 2(1), 11–21 (2011)
Horrocks, I., Kutz, O., Sattler, U.: The even more irresistible \(\cal{SROIQ}\). In: Proceedings of KR 2006, pp. 57–67. AAAI Press (2006)
Jifeng, H., Seidel, K., McIver, A.: Probabilistic models for the guarded command language. Sci. Comput. Program. 28(2), 171–192 (1997)
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)
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)
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_47
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
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)
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_9
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/
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)
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)
Poggi, A., Lembo, D., Calvanese, D., De Giacomo, G., Lenzerini, M., Rosati, R.: Linking data to ontologies. J. Data Semant. 4900, 133–173 (2008)
Puterman, M.: Markov Decision Processes: Discrete Stochastic Dynamic Programming. Wiley, New York (1994)
Rudolph, S., Glimm, B.: Nominals, inverses, counting, and conjunctive queries or: why infinity is your friend!. J. Artif. Intell. Res. 39, 429–481 (2010)
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)
Tobies, S.: Complexity results and practical algorithms for logics in knowledge representation. Ph.D. thesis, RWTH Aachen University, Germany (2001)
Zarrieß, B., Claßen, J.: Verification of knowledge-based programs over description logic actions. In: IJCAI, pp. 3278–3284. AAAI Press (2015)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Dubslaff, C., Koopmann, P., Turhan, AY. (2019). Ontology-Mediated Probabilistic Model Checking. In: Ahrendt, W., Tapia Tarifa, S. (eds) Integrated Formal Methods. IFM 2019. Lecture Notes in Computer Science(), vol 11918. Springer, Cham. https://doi.org/10.1007/978-3-030-34968-4_11
Download citation
DOI: https://doi.org/10.1007/978-3-030-34968-4_11
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-34967-7
Online ISBN: 978-3-030-34968-4
eBook Packages: Computer ScienceComputer Science (R0)