Models for Incomplete and Probabilistic Information

We discuss, compare and relate some old and some new models for incomplete and probabilistic databases. We characterize the expressive power of c-tables over infinite domains and we introduce a new kind of result, algebraic completion, for studying less expressive models. By viewing probabilistic models as incompleteness models with additional probability information, we define completeness and closure under query languages of general probabilistic database models and we introduce a new such model, probabilistic c-tables, that is shown to be complete and closed under the relational algebra.

[1]  Ronald Fagin,et al.  Data exchange: semantics and query answering , 2005, Theor. Comput. Sci..

[2]  Serge Abiteboul,et al.  Complexity of answering queries using materialized views , 1998, PODS.

[3]  Val Tannen,et al.  Update Exchange with Mappings and Provenance , 2007, VLDB.

[4]  Raymond Reiter,et al.  A sound and sometimes complete query evaluation algorithm for relational databases with null values , 1986, JACM.

[5]  Dan Suciu,et al.  Foundations of probabilistic answers to queries , 2005, SIGMOD '05.

[6]  Esteban Zimányi,et al.  Query Evaluation in Probabilistic Relational Databases , 1997, Theor. Comput. Sci..

[7]  Dan Suciu,et al.  Efficient query evaluation on probabilistic databases , 2004, The VLDB journal.

[8]  Jennifer Widom,et al.  Trio: A System for Integrated Management of Data, Accuracy, and Lineage , 2004, CIDR.

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

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

[11]  Limsoon Wong,et al.  Semantic representations and query languages for or-sets , 1993, PODS '93.

[12]  Sanjeev Khanna,et al.  Why and Where: A Characterization of Data Provenance , 2001, ICDT.

[13]  Moshe Y. Vardi.  Querying logical databases , 1985, J. Comput. Syst. Sci..

[14]  V. S. Subrahmanian,et al.  Optimal models of disjunctive logic programs: semantics, complexity, and computation , 2004, IEEE Transactions on Knowledge and Data Engineering.

[15]  Leonid Libkin,et al.  Aspects of partial information in databases , 1995 .

[16]  Alain Pirotte,et al.  Imperfect Information in Relational Databases , 1996, Uncertainty Management in Information Systems.

[17]  Joseph Y. Halpern.  Reasoning about uncertainty , 2003 .

[18]  Raghu Ramakrishnan,et al.  Containment of conjunctive queries: beyond relations as sets , 1995, TODS.

[19]  Dan Olteanu,et al.  Fast and Simple Relational Processing of Uncertain Data , 2007, 2008 IEEE 24th International Conference on Data Engineering.

[20]  Norbert Fuhr,et al.  A probabilistic relational algebra for the integration of information retrieval and database systems , 1997, TOIS.

[21]  Mihalis Yannakakis,et al.  Equivalences Among Relational Expressions with the Union and Difference Operators , 1980, J. ACM.

[22]  Jennifer Widom,et al.  ULDBs: databases with uncertainty and lineage , 2006, VLDB.

[23]  Fereidoon Sadri,et al.  Modeling uncertainty in databases , 1991, [1991] Proceedings. Seventh International Conference on Data Engineering.

[24]  Jennifer Widom,et al.  Tracing the lineage of view data in a warehousing environment , 2000, TODS.

[25]  Jennifer Widom,et al.  Lineage tracing in data warehouses , 2001 .

[26]  Gösta Grahne,et al.  The Problem of Incomplete Information in Relational Databases , 1991, Lecture Notes in Computer Science.

[27]  Serge Abiteboul,et al.  Foundations of Databases , 1994 .

[28]  Ron van der Meyden,et al.  Logical Approaches to Incomplete Information: A Survey , 1998, Logics for Databases and Information Systems.

[29]  Serge Abiteboul,et al.  On the representation and querying of sets of possible worlds , 1987, SIGMOD '87.

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

[31]  Ashok K. Chandra,et al.  Optimal implementation of conjunctive queries in relational data bases , 1977, STOC '77.

[32]  R. P. Dilworth,et al.  Algebraic theory of lattices , 1973 .

[33]  Jennifer Widom,et al.  Working Models for Uncertain Data , 2006, 22nd International Conference on Data Engineering (ICDE'06).

[34]  Christopher Ré,et al.  Query Evaluation on Probabilistic Databases , 2006, IEEE Data Eng. Bull..

[35]  Gösta Grahne.  Horn tables-an efficient tool for handling incomplete information in databases , 1989, PODS '89.

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

[37]  Yuri Gurevich,et al.  The complexity of query reliability , 1998, PODS.

[38]  R. Durrett.  Probability: Theory and Examples , 1993 .

[39]  Ben Taskar,et al.  Learning Probabilistic Models of Relational Structure , 2001, ICML.

[40]  Lise Getoor,et al.  Learning Probabilistic Relational Models with Structural Uncertainty , 2000 .

[41]  Jan Chomicki,et al.  Answer sets for consistent query answering in inconsistent databases , 2002, Theory and Practice of Logic Programming.

[42]  Wang Chiew Tan,et al.  Debugging schema mappings with routes , 2006, VLDB.

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

[44]  Tomasz Imielinski,et al.  Incomplete Information in Relational Databases , 1984, JACM.

[45]  Tomasz Imielinski,et al.  Incomplete object—a data model for design and planning applications , 1991, SIGMOD '91.

[46]  Hector Garcia-Molina,et al.  A Probalilistic Relational Data Model , 1990, EDBT.