This Article 
 Bibliographic References 
 Add to: 
Temporal Probabilistic Object Bases
July/August 2003 (vol. 15 no. 4)
pp. 921-939

Abstract—There are numerous applications where we have to deal with temporal uncertainty associated with objects. The ability to automatically store and manipulate time, probabilities, and objects is important. We propose a data model and algebra for temporal probabilistic object bases (TPOBs), which allows us to specify the probability with which an event occurs at a given time point. In explicit TPOB-instances, the sets of time points along with their probability intervals are explicitly enumerated. In implicit TPOB-instances, sets of time points are expressed by constraints and their probability intervals by probability distribution functions. Thus, implicit object base instances are succinct representations of explicit ones; they allow for an efficient implementation of algebraic operations, while their explicit counterparts make defining algebraic operations easy. We extend the relational algebra to both explicit and implicit instances and prove that the operations on implicit instances correctly implement their counterpart on explicit instances.

[1] S. Abiteboul, R. Hull, and V. Vianu, Foundations of Databases. Reading, Mass.: Addison-Wesley, 1995.
[2] S. Adali and L. Pigaty, The DARPA Advanced Logistics Program Annals of Math. and Artificial Intelligence, vol. 37, no. 4, pp. 409-452, 2003.
[3] E.I. Altman, Financial Ratios, Discriminant Analysis, and the Prediction of a Corporate Bankruptcy J. Finance, vol. 23, pp. 589-609, 1968.
[4] M. Atkinson, D. DeWitt, D. Maier, F. Bancilhon, K. Dittrich, and S. Zdonik, The Object-Oriented Database System Manifesto Proc. Deductive and Object-Oriented Databases Conf., Elsevier Science Publishers, pp. 223-240, 1990.
[5] Building an Object-Oriented Database System: The Story of$O_2$. F. Bancilhon, C. Delobel, and P. Kanellakis, eds. Los Altos, Calif.: Morgan Kaufmann, 1991.
[6] V. Biazzo, R. Giugno, T. Lukasiewicz, and V.S. Subrahmanian, Temporal Probabilistic Object Bases Technical Report INFSYS RR-1843-02-08, Institut für Informationssysteme, TU Wien, rr0208.pdf, 2002.
[7] P.A. Boncz, A.N. Wilschut, and M.L. Kersten, Flattening an Object Algebra to Provide Performance Proc. Int'l Conf. Data Eng., pp. 568-577, 1998.
[8] G. Boole, The Laws of Thought. London: Macmillan, 1854.
[9] V. Brusoni, L. Console, P. Terenziani, and B. Pernici, Extending Temporal Relational Databases to Deal with Imprecise and Qualitative Temporal Information Recent Advances in Temporal Databases, pp. 3-22, Springer, 1995.
[10] J.B. Caouette, E.I. Altman, and P. Narayanan, Managing Credit Risk: The Next Great Financial Challenge. John Wiley, 1998.
[11] Y.F. Day, S. Dagtas, M. Iino, A. Khokhar, and A. Ghafoor, “Object-Oriented Conceptual Modeling of Video Data,” Proc. Data Eng. (DE '95), pp. 401-408, 1995.
[12] Y.F. Day, S. Dagstas, and A. Ghafoor, “Spatio-Temporal Modeling of Video Data for On-Line Object-Oriented Query Processing,” Proc. IEEE Int'l Conf. Multimedia (ICMCS '95), pp. 98-105, 1995.
[13] A. Dekhtyar, R. Ross, and V.S. Subrahmanian, Probabilistic Temporal Databases, I: Algebra ACM Trans. Database Systems, vol. 26, no. 1, pp. 41-95, 2001.
[14] D.J. Dewitt, N. Kabra, J. Luo, J. Patel, and J. Yu, Client-Server Paradise Proc. Very Large Data Bases Conf., pp. 558-569, 1994.
[15] D. Dey and S. Sarkar, A Probabilistic Relational Model and Algebra ACM Trans. Database Systems, vol. 21, no. 3, pp. 339-369, 1996.
[16] D. Dubois and H. Prade, “Processing Fuzzy Temporal Knowledge,” IEEE Trans. Systems, Man, and Cybernetics, vol. 19, pp. 729-744, 1989.
[17] S. Dutta, Generalized Events in Temporal Databases Proc. Int'l Conf. Data Eng., pp. 118-126, 1989.
[18] C. Dyreson and R. Snodgrass, Supporting Valid-Time Indeterminacy ACM Trans. Database Systems, vol. 23, no. 1, pp. 1-57, 1998.
[19] T. Eiter, J.J. Lu, T. Lukasiewicz, and V.S. Subrahmanian, Probabilistic Object Bases ACM Trans. Database Systems, vol. 26, no. 3, pp. 264-312, 2001.
[20] T. Eiter, T. Lukasiewicz, and M. Walter, A Data Model and Algebra for Probabilistic Complex Values Annals of Math. and Artificial Intelligence, vol. 33, nos. 2-4, pp. 205-252, 2001.
[21] R. Fagin, J.Y. Halpern, and N. Megiddo, A Logic for Reasoning About Probabilities Information and Computation, vol. 87, nos. 1-2, pp. 78-128, 1990.
[22] S. Gadia, S. Nair, and Y.C. Poon, Incomplete Information in Relational Temporal Databases Proc. Very Large Data Bases Conf., Morgan Kaufmann, pp. 395-406, 1992.
[23] I. Goralwalla, Y. Leontiev, M.T. Özsu, D. Szafron, and C. Combi, Temporal Granularity: Completing the Puzzle J. Intelligent Information Systems, vol. 16, no. 1, pp. 41-63, 2001.
[24] C.S. Jensen and R.T. Snodgrass, “Temporal Data Management,” IEEE Trans. Knowledge and Data Eng., vol. 11, no. 1, pp. 36–45, 1999.
[25] S. Khoshafian, The Jasmine Object-Oriented Database: Multimedia Applications for the Web. Morgan Kaufman, 1998.
[26] Y. Kornatzky and S.E. Shimony, A Probabilistic Object-Oriented Data Model Data and Knowledge Eng., vol. 12, pp. 143-166, 1994.
[27] Y. Kornatzky and S.E. Shimony, A Probabilistic Spatial Data Model Information Sciences, vol. 90, pp. 51-74, 1996.
[28] M. Koubarakis, Complexity Results for First-Order Theories of Temporal Constraints Proc. Fourth Int'l Conf. Principles of Knowledge Representation and Reasoning, pp. 379-390, 1994.
[29] M. Koubarakis, Database Models for Infinite and Indefinite Temporal Information Information Systems, vol. 19, no. 2, pp. 141-173, 1994.
[30] S. Kraus, Y. Sagiv, and V.S. Subrahmanian, Representing and Integrating Multiple Calendars Technical Report CS-TR-3751, Univ. of Maryland, 1996.
[31] H.E. Kyburg, Jr., Interval-Valued Probabilities Imprecise Probabilities Project, G. de Cooman, P. Walley, and F.G. Cozman, eds., available fromhttp:/, 1998.
[32] L.V.S. Lakshmanan, N. Leone, R. Ross, and V.S. Subrahmanian, ProbView: A Flexible Probabilistic Database System ACM Trans. Database Systems, vol. 22, no. 3, pp. 419-469, 1997.
[33] L.V.S. Lakshmanan and F. Sadri, Modeling Uncertainty in Deductive Databases Proc. Database and Expert Systems Applications Workshop, pp. 724-733, 1994.
[34] L.V.S. Lakshmanan and N. Shiri, A Parametric Approach to Deductive Databases with Uncertainty IEEE Trans. Knowledge and Data Eng., vol. 13, no. 4, pp. 554-570, July/Aug. 2001.
[35] G. Özsoyovglu and R.T. Snodgrass, “Temporal and Real-Time Databases: A Survey,” IEEE Trans. Knowledge and Data Eng., vol. 7, no. 4, pp. 513–532, 1995.
[36] S. Ross, A First Course in Probability. Prentice Hall, 2001.
[37] H.-J. Schek and P. Pistor, Data Structures for an Integrated Data Base Management and Information Retrieval System Proc. Very Large Data Bases Conf., pp. 197-207, 1982.
[38] G. Shaw and S. Zdonik,“A query algebra for object-oriented databases,” Proc. Sixth Int’l Conf. Data Eng., pp. 154-162, Feb. 1990.
[39] N. Shiri, On a Generalized Theory of Deductive Databases PhD thesis, Concordia Univ., Montreal, Canada, Aug. 1997.
[40] R.T. Snodgrass, Monitoring Distributed Systems: A Relational Approach PhD thesis, Carnegie Mellon Univ., 1982.
[41] R.T. Snodgrass, Temporal Object-Oriented Databases: A Critical Comparison Modern Database Systems: The Object Model, Interoperability and Beyond, W. Kim, ed., ACM Press/Addison-Wesley, 1995.
[42] B. Subramanian, T.W. Leung, S.L. Vandenberg, and S.B. Zdonik, "The Aqua Approach to Querying Lists and Trees in Object-Oriented Databases," Proc. IEEE Int'l Conf. Data Eng., 1995.
[43] D. Suciu and J. Paredaens, Any Algorithm in the Complex Object Algebra with Powerset Needs Exponential Space to Compute Transitive Closure Proc. Principles of Database Systems Conf., pp. 201-209, 1994.
[44] Temporal Databases: Theory, Design, and Implementation. A. Tansel, J. Clifford, S. Gadia, S. Jajodia, A. Segev, and R.T. Snodgrass, eds., Benjamin/Cummings, 1994.
[45] S.L. Vendenberg and D.J. Dewitt, Algebraic Support for Complex Objects with Arrays, Identity and Inheritance Proc. SIGMOD, pp. 158-167, 1991.

Index Terms:
Probabilistic databases, uncertainty management, temporal data.
Veronica Biazzo, Rosalba Giugno, Thomas Lukasiewicz, V.S. Subrahmanian, "Temporal Probabilistic Object Bases," IEEE Transactions on Knowledge and Data Engineering, vol. 15, no. 4, pp. 921-939, July-Aug. 2003, doi:10.1109/TKDE.2003.1209009
Usage of this product signifies your acceptance of the Terms of Use.