Count Queries in Probabilistic Spatio-Temporal Knowledge Bases with Capacity Constraints

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10369)


The problem of managing spatio-temporal data arises in many applications, such as location-based services, environment monitoring, geographic information system, and many others. In real life, this kind of data is often uncertain. The SPOT framework has been proposed for the representation and processing of probabilistic spatio-temporal data where probability is represented as an interval because the exact value is unknown.

In this paper, we enhance the SPOT framework with capacity constraints, which allow users to better model many real-world scenarios. The resulting formalization is called PST knowledge base. We study the computational complexity of consistency checking, a central problem in this setting. Specifically, we show that the problem is NP-complete and also identify tractable cases. We then consider a relevant kind of queries to reason on PST knowledge bases, namely count queries, which ask for how many objects are in a region at a certain time point. We investigate the computational complexity of answering count queries, and show cases for which consistency checking can be exploited for query answering.


Capacity Constraint Consistency Check Inside Region Query Answering Declarative Language 
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.


  1. 1.
    Agarwal, P.K., Arge, L., Erickson, J.: Indexing moving points. J. Comput. Syst. Sci. 66(1), 207–243 (2003)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Ahson, S.A., Ilyas, M.: Location-Based Services Handbook: Applications, Technologies, and Security. CRC Press, Hoboken (2010)CrossRefGoogle Scholar
  3. 3.
    Akdere, M., Cetintemel, U., Riondato, M., Upfal, E., Zdonik, S.B.: The case for predictive database systems: opportunities and challenges. In: Proceedings of the 5th Biennial Conference on Innovative Data Systems Research (CIDR), pp. 167–174 (2011)Google Scholar
  4. 4.
    Bayir, M.A., Demirbas, M., Eagle, N.: Mobility profiler: a framework for discovering mobility profiles of cell phone users. Pervasive Mob. Comput. 6(4), 435–454 (2010)CrossRefGoogle Scholar
  5. 5.
    Cohn, A.G., Hazarika, S.M.: Qualitative spatial representation and reasoning: an overview. Fundamenta Informaticae 46(1–2), 1–29 (2001)MathSciNetMATHGoogle Scholar
  6. 6.
    Doder, D., Grant, J., Ognjanović, Z.: Probabilistic logics for objects located in space and time. J. Logic Comput. 23(3), 487–515 (2013)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Dousson, C., Maigat, P.L.: Chronicle recognition improvement using temporal focusing and hierarchization. In: Proceedings of International Joint Conference on Artificial Intelligence (IJCAI), pp. 324–329 (2007)Google Scholar
  8. 8.
    Gabelaia, D., Kontchakov, R., Kurucz, Á., Wolter, F., Zakharyaschev, M.: Combining spatial and temporal logics: expressiveness vs. complexity. J. Artif. Intell. Res. 23, 167–243 (2005)MathSciNetMATHGoogle Scholar
  9. 9.
    Grant, J., Molinaro, C., Parisi, F.: Aggregate count queries in probabilistic spatio-temporal databases. In: Liu, W., Subrahmanian, V.S., Wijsen, J. (eds.) SUM 2013. LNCS (LNAI), vol. 8078, pp. 255–268. Springer, Heidelberg (2013). doi: 10.1007/978-3-642-40381-1_20 CrossRefGoogle Scholar
  10. 10.
    Grant, J., Parisi, F., Parker, A., Subrahmanian, V.S.: An AGM-style belief revision mechanism for probabilistic spatio-temporal logics. Artif. Intell. 174(1), 72–104 (2010)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Grant, J., Parisi, F., Subrahmanian, V.S.: Research in probabilistic spatiotemporal databases: the SPOT framework. In: Ma, Z., Yan, L. (eds.) Advances in Probabilistic Databases for Uncertain Information Management, Studies in Fuzziness and Soft Computing, vol. 304, pp. 1–22. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  12. 12.
    Hammel, T., Rogers, T.J., Yetso, B.: Fusing live sensor data into situational multimedia views. In: Proceedings of International Workshop on Multimedia Information Systems, pp. 145–156 (2003)Google Scholar
  13. 13.
    Karbassi, A., Barth, M.: Vehicle route prediction and time of arrival estimation techniques for improved transportation system management. In: Proceedings of the 2013 IEEE Intelligent Vehicles Symposium, pp. 511–516 (2003)Google Scholar
  14. 14.
    Karimi, H.A.: Advanced Location-Based Technologies and Services. CRC Press, Boca Raton (2013)CrossRefGoogle Scholar
  15. 15.
    Kurkovsky, S., Harihar, K.: Using ubiquitous computing in interactive mobile marketing. Pers. Ubiquit. Comput. 10(4), 227–240 (2006)CrossRefGoogle Scholar
  16. 16.
  17. 17.
    Mittu, R., Ross, R.: Building upon the coalitions agent experiment (CoAX) - integration of multimedia information in GCCS-M using impact. In: Proceedings of International Workshop on Multimedia Information Systems (MIS), pp. 35–44 (2003)Google Scholar
  18. 18.
    Parisi, F., Grant, J.: Knowledge representation in probabilistic spatio-temporal knowledge bases. J. Artif. Intell. Res. (JAIR) 55, 743–798 (2016)MathSciNetMATHGoogle Scholar
  19. 19.
    Parisi, F., Grant, J.: On repairing and querying inconsistent probabilistic spatio-temporal databases. Int. J. Approx. Reason. (IJAR) 84, 41–74 (2017)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Parisi, F., Parker, A., Grant, J., Subrahmanian, V.S.: Scaling cautious selection in spatial probabilistic temporal databases. In: Jeansoulin, R., Papini, O., Prade, H., Schockaert, S. (eds.) Methods for Handling Imperfect Spatial Information, Studies in Fuzziness and Soft Computing, vol. 256, pp. 307–340. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  21. 21.
    Parisi, F., Sliva, A., Subrahmanian, V.S.: A temporal database forecasting algebra. Int. J. Approx. Reason. 54(7), 827–860 (2013)MathSciNetCrossRefMATHGoogle Scholar
  22. 22.
    Parker, A., Infantes, G., Grant, J., Subrahmanian, V.S.: SPOT databases: efficient consistency checking and optimistic selection in probabilistic spatial databases. IEEE Trans. Knowl. Data Eng. (TKDE) 21(1), 92–107 (2009)CrossRefGoogle Scholar
  23. 23.
    Parker, A., Infantes, G., Subrahmanian, V.S., Grant, J.: An AGM-based belief revision mechanism for probabilistic spatio-temporal logics. In: Proceedings of AAAI Conference on Artificial Intelligence (AAAI), pp. 511–516 (2008)Google Scholar
  24. 24.
    Parker, A., Subrahmanian, V.S., Grant, J.: A logical formulation of probabilistic spatial databases. IEEE Trans. Knowl. Data Eng. (TKDE) 19(11), 1541–1556 (2007)CrossRefGoogle Scholar
  25. 25.
    Parker, A., Yaman, F., Nau, D.S., Subrahmanian, V.S.: Probabilistic go theories. In: Proceedings of International Joint Conference on Artificial Intelligence (IJCAI), pp. 501–506 (2007)Google Scholar
  26. 26.
    Pelanis, M., Saltenis, S., Jensen, C.S.: Indexing the past, present, and anticipated future positions of moving objects. ACM Trans. Database Syst. 31(1), 255–298 (2006)CrossRefGoogle Scholar
  27. 27.
    Saint-Cyr, F.D., Lang, J.: Reasoning about unpredicted change and explicit time. In: Gabbay, D.M., Kruse, R., Nonnengart, A., Ohlbach, H.J. (eds.) ECSQARU/FAPR -1997. LNCS, vol. 1244, pp. 223–236. Springer, Heidelberg (1997). doi: 10.1007/BFb0035625 CrossRefGoogle Scholar
  28. 28.
    de Saint-Cyr, F.D., Lang, J.: Belief extrapolation (or how to reason about observations and unpredicted change). Artif. Intell. 175(2), 760–790 (2011)MathSciNetCrossRefMATHGoogle Scholar
  29. 29.
    Southey, F., Loh, W., Wilkinson, D.F.: Inferring complex agent motions from partial trajectory observations. In: Proceedings of International Joint Conference on Artificial Intelligence (IJCAI), pp. 2631–2637 (2007)Google Scholar
  30. 30.
    Tao, Y., Cheng, R., Xiao, X., Ngai, W.K., Kao, B., Prabhakar, S.: Indexing multi-dimensional uncertain data with arbitrary probability density functions. In: Proceedings of International Conference on Very Large Data Bases (VLDB), pp. 922–933 (2005)Google Scholar
  31. 31.
    Yaman, F., Nau, D.S., Subrahmanian, V.S.: A logic of motion. In: Proceedings of International Conference on Principles of Knowledge Representation and Reasoning (KR), pp. 85–94 (2004)Google Scholar
  32. 32.
    Yaman, F., Nau, D.S., Subrahmanian, V.S.: Going far, logically. In: Proceedings of International Joint Conference on Artificial Intelligence (IJCAI), pp. 615–620 (2005)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • John Grant
    • 1
  • Cristian Molinaro
    • 2
  • Francesco Parisi
    • 2
  1. 1.University of MarylandCollege ParkUSA
  2. 2.DIMES DepartmentUniversità della CalabriaRendeItaly

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