Probabilistic interval XML

Interest in XML databases has been expanding rapidly over the last few years. In this paper, we study the problem of incorporating probabilistic information into XML databases. We propose the Probabilistic Interval XML (PIXML for short) data model in this paper. Using this data model, users can express probabilistic information within XML markups. In addition, we provide two alternative formal model-theoretic semantics for PIXML data. The first semantics is a “global” semantics which is relatively intuitive, but is not directly amenable to computation. The second semantics is a “local” semantics which supports efficient computation. We prove several correspondence results between the two semantics. To our knowledge, this is the first formal model theoretic semantics for probabilistic interval XML. We then provide an operational semantics that may be used to compute answers to queries and that is correct for a large class of probabilistic instances.

[1]  Werner Kießling,et al.  Database Support for Problematic Knowledge , 1992, EDBT.

[2]  Thomas Lukasiewicz,et al.  Probabilistic object bases , 2001, TODS.

[3]  V. S. Subrahmanian,et al.  PXML: a probabilistic semistructured data model and algebra , 2003, Proceedings 19th International Conference on Data Engineering (Cat. No.03CH37405).

[4]  H. V. Jagadish,et al.  ProTDB: Probabilistic Data in XML , 2002, VLDB.

[5]  Alex Dekhtyar,et al.  Semistructured probabilistic databases , 2001, Proceedings Thirteenth International Conference on Scientific and Statistical Database Management. SSDBM 2001.

[6]  Alex Dekhtyar,et al.  Databases for interval probabilities: Research Articles , 2004 .

[7]  Alex Dekhtyar,et al.  Query Algebra Operations for Interval Probabilities , 2003, DEXA.

[8]  Serafín Moral,et al.  Strong Conditional Independence for Credal Sets , 2004, Annals of Mathematics and Artificial Intelligence.

[9]  Laks V. S. Lakshmanan,et al.  A Parametric Approach to Deductive Databases with Uncertainty , 1996, Logic in Databases.

[10]  David Poole,et al.  First-order probabilistic inference , 2003, IJCAI.

[11]  Avi Pfeffer,et al.  Object-Oriented Bayesian Networks , 1997, UAI.

[12]  Ronald Fagin,et al.  A logic for reasoning about probabilities , 1988, [1988] Proceedings. Third Annual Information Symposium on Logic in Computer Science.

[13]  Laks V. S. Lakshmanan,et al.  ProbView: a flexible probabilistic database system , 1997, TODS.

[14]  E. Ziegel.  Forecasting and Time Series: An Applied Approach , 2000 .

[15]  Hector Garcia-Molina,et al.  The Management of Probabilistic Data , 1992, IEEE Trans. Knowl. Data Eng..

[16]  Sumit Sarkar,et al.  A probabilistic relational model and algebra , 1996, TODS.

[17]  Curtis E. Dyreson,et al.  Supporting valid-time indeterminacy , 1998, TODS.

[18]  Michael Pittarelli,et al.  The Theory of Probabilistic Databases , 1987, VLDB.

[19]  Laks V. S. Lakshmanan,et al.  Probabilistic Deductive Databases , 1994, ILPS.

[20]  B. Bowerman,et al.  Forecasting and Time Series: An Applied Approach , 2000 .

[21]  Alex Dekhtyar,et al.  Databases for interval probabilities , 2004, Int. J. Intell. Syst..

[22]  Harris Wu,et al.  Probabilistic question answering on the web , 2002, WWW '02.

[23]  Avi Pfeffer,et al.  Probabilistic Frame-Based Systems , 1998, AAAI/IAAI.

[24]  Daniel Kahneman,et al.  Probabilistic reasoning , 1993 .

[25]  Nir Friedman,et al.  Being Bayesian About Network Structure. A Bayesian Approach to Structure Discovery in Bayesian Networks , 2004, Machine Learning.

[26]  Ronald L. Rivest,et al.  A non-iterative maximum entropy algorithm , 1986, UAI.

[27]  Laks V. S. Lakshmanan,et al.  A Parametric Approach to Deductive Databases with Uncertainty , 2001, IEEE Trans. Knowl. Data Eng..

[28]  George Boole,et al.  The Laws of Thought , 2003 .

[29]  Werner Kießling,et al.  New direction for uncertainty reasoning in deductive databases , 1991, SIGMOD '91.

[30]  Roy Goldman,et al.  Lore: a database management system for semistructured data , 1997, SGMD.

[31]  Lise Getoor,et al.  Learning Probabilistic Relational Models , 1999, IJCAI.

[32]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems , 1988 .

[33]  Alex Dekhtyar,et al.  Can Probabilistic Databases Help Elect Qualified Officials? , 2003, FLAIRS.

[34]  Luc De Raedt,et al.  Adaptive Bayesian Logic Programs , 2001, ILP.

[35]  Serafín Moral,et al.  Building classification trees using the total uncertainty criterion , 2003, Int. J. Intell. Syst..

[36]  C. M. Sperberg-McQueen,et al.  Extensible Markup Language (XML) , 1997, World Wide Web J..

[37]  Dan Roth,et al.  Lifted First-Order Probabilistic Inference , 2005, IJCAI.

[38]  DeyDebabrata,et al.  A probabilistic relational model and algebra , 1996 .

[39]  Max Mintz,et al.  Stereo depth estimation: a confidence interval approach , 1998, Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271).

[40]  Nevin Lianwen Zhang,et al.  Exploiting Contextual Independence In Probabilistic Inference , 2011, J. Artif. Intell. Res..