On the Representation and Querying of Sets of Possible Worlds

Abstract We represent a set of possible worlds using an incomplete information database. The representation techniques that we study range from the very simple Codd-table (a relation over constants and uniquely occurring variables called nulls) to much more complex mechanisms involving views of conditioned-tables (programs applied to Codd-tables augmented by equality and inequality conditions). (1) We provide matching upper and lower bounds on the data-complexity of testing containment, membership and uniqueness for sets of possible worlds. We fully classify these problems with respect to our representations. (2) We investigate the data-complexity of querying incomplete information databases for both possible and certain facts. For each fixed positive existential query on conditioned-tables we present a polynomial time algorithm solving the possible fact problem. We match this upper bound by two NP-completeness lower bounds, when the fixed query contains either negation or recursion and is applied to Codd-tables. Finally, we show that the certain fact problem is coNP-complete, even for a fixed first order query applied to a Codd-table.

[1]  Stavros S. Cosmadakis.  The Complexity of Evaluating Relational Queries , 1983, Inf. Control..

[2]  David Harel,et al.  Horn Clauses Queries and Generalizations , 1985, J. Log. Program..

[3]  Mihalis Yannakakis,et al.  On the Complexity of Testing Implications of Functional and Join Dependencies , 1981, JACM.

[4]  Mihalis Yannakakis,et al.  Testing the Universal Instance Assumption , 1980, Inf. Process. Lett..

[5]  Witold Lipski,et al.  On Databases with Incomplete Information , 1981, JACM.

[6]  Serge Abiteboul,et al.  Update Semantics for Incomplete Databases , 1985, VLDB.

[7]  Moshe Y. Vardi.  Querying Logical Databases , 1986, J. Comput. Syst. Sci..

[8]  Larry J. Stockmeyer,et al.  The Polynomial-Time Hierarchy , 1976, Theor. Comput. Sci..

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

[10]  David Harel,et al.  Structure and complexity of relational queries , 1980, 21st Annual Symposium on Foundations of Computer Science (sfcs 1980).

[11]  Tomasz Imielinski.  On Algebraic Query Processing in Logical Databases , 1982, Advances in Data Base Theory.

[12]  Gösta Grahne,et al.  Dependency Satisfaction in Databases with Incomplete Information , 1984, VLDB.

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

[14]  E. F. Codd,et al.  Extending the database relational model to capture more meaning , 1979, ACM Trans. Database Syst..

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