Incomplete Information

DEFINITION Incomplete information arises in relational databases, when a fact (tuple) has to be inserted in a relation, and values for some required columns are missing. For instance, in an employee database, the phone number of one employee might be missing, as might also the address of another employee. There are numerous reasons for such missing information, e.g. the insertion was done through a view, or the incomplete tuple originated from another database that does not record these fields. In information integration and data exchange systems incomplete information is rampant. Note that here the null values only represent unknown, existing values. The other main case, namely the one that the column heading is not applicable to the tuple in question, is not covered here, for a treatment, see e.g. [14]. It is easy to store missing or incomplete information, by simply using a symbol, say ⊥, different from the symbols of the domain of the database. As an illustration, consider the following employee database:

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

[2]  Gösta Grahne,et al.  Towards an algebraic theory of information integration , 2004, Inf. Comput..

[3]  Leonid Libkin,et al.  Data exchange and incomplete information , 2006, PODS '06.

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

[5]  Alberto O. Mendelzon,et al.  Tableau Techniques for Querying Information Sources through Global Schemas , 1999, ICDT.

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

[7]  Tomasz Imielinski,et al.  Complexity of query processing in databases with OR-objects , 1989, PODS '89.

[8]  Witold Lipski.  On Relational Algebra with Marked Nulls. , 1984, PODS 1984.

[9]  Yannis Vassiliou,et al.  Null values in data base management a denotational semantics approach , 1979, SIGMOD '79.

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

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

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

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

[14]  Serge Abiteboul,et al.  Representing and querying XML with incomplete information , 2001, PODS '01.

[15]  Peter Z. Revesz,et al.  Introduction to Constraint Databases , 2002, Texts in Computer Science.

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