Data exchange and incomplete information

Data exchange is the problem of finding an instance of a target schema, given an instance of a source schema and a specification of the relationship between the source and the target, and answering queries over target instances in a way that is semantically consistent with the information in the source. Theoretical foundations of data exchange have been actively explored recently. It was also noticed that the standard certain answers semantics may behave in very odd ways.In this paper I explain that this behavior is due to the fact that the presence of incomplete information in target instances has been ignored; in particular, proper query evaluation techniques for databases with nulls have not been used, and the distinction between closed and open world semantics has not been made. I present a concept of target solutions based on the closed world assumption, and show that the space of all solutions has two extreme points: the canonical universal solution and the core, well studied in data exchange. I show how to define semantics of query answering taking into account incomplete information, and show that the well-known anomalies go away with the new semantics. The paper also contains results on the complexity of query answering, upper approximations to queries (maybe-answers), and various extensions.

[1]  Mark Levene,et al.  Axiomatisation of Functional Dependencies in Incomplete Relations , 1998, Theor. Comput. Sci..

[2]  Peter Buneman,et al.  Using Powerdomains to Generalize Relational Databases , 1991, Theor. Comput. Sci..

[3]  Aleksander Madry,et al.  Data exchange: On the complexity of answering queries with inequalities , 2005, Inf. Process. Lett..

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

[5]  Mark Levene,et al.  Null Inclusion Dependencies in Relational Databases , 1997, Inf. Comput..

[6]  Ronald Fagin,et al.  Data exchange: semantics and query answering , 2003, Theor. Comput. Sci..

[7]  Jaroslav Nesetril,et al.  The core of a graph , 1992, Discret. Math..

[8]  Phokion G. Kolaitis.  Schema mappings, data exchange, and metadata management , 2005, PODS '05.

[9]  Laura M. Haas,et al.  The Clio project: managing heterogeneity , 2001, SGMD.

[10]  Serge Abiteboul,et al.  On the Representation and Querying of Sets of Possible Worlds , 1991, Theor. Comput. Sci..

[11]  Carl A. Gunter,et al.  The Mixed Powerdomain , 2008 .

[12]  Jan Chomicki,et al.  Consistent query answers in inconsistent databases , 1999, PODS '99.

[13]  Leonid Libkin,et al.  Models of Approximation in Databases , 1998, Theor. Comput. Sci..

[14]  Jan Chomicki,et al.  Exchange, integration, and consistency of data: report on the ARISE/NISR workshop , 2005, SGMD.

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

[16]  Georg Gottlob,et al.  Closed World Databases Opened Through Null Values , 1988, VLDB.

[17]  Carlo Zaniolo,et al.  Database relations with null values , 1982, J. Comput. Syst. Sci..

[18]  Witold Lipski,et al.  On semantic issues connected with incomplete information databases , 1979, ACM Trans. Database Syst..

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

[20]  李幼升,et al.  Ph , 1989 .

[21]  Ronald Fagin,et al.  Translating Web Data , 2002, VLDB.

[22]  Moshe Y. Vardi.  On the integrity of databases with incomplete information , 1985, PODS.

[23]  Georg Gottlob,et al.  Computing cores for data exchange: new algorithms and practical solutions , 2005, PODS '05.

[24]  Vincent Y. Lum,et al.  EXPRESS: a data EXtraction, Processing, and Restructuring System , 1977, TODS.

[25]  Marcelo Arenas,et al.  XML data exchange: consistency and query answering , 2005, PODS '05.

[26]  Ronald Fagin,et al.  Composing schema mappings: second-order dependencies to the rescue , 2004, PODS '04.

[27]  References , 1971 .

[28]  Ronald Fagin,et al.  Locally consistent transformations and query answering in data exchange , 2004, PODS '04.

[29]  Johann Eder,et al.  Logic and Databases , 1992, Advanced Topics in Artificial Intelligence.

[30]  Aaron Watters,et al.  A Semantics for Complex Objects and Approximate Answers , 1991, J. Comput. Syst. Sci..

[31]  Raymond Reiter,et al.  Towards a Logical Reconstruction of Relational Database Theory , 1982, On Conceptual Modelling.