On Decidability and Complexity of Description Logics with Uniqueness Constraints

We establish the equivalence of: (1) the logical implication problem for a description logic dialect called DLClass that includes a concept constructor for expressing uniqueness constraints, (2) the logical implication problem for path functional dependencies (PFDs), and (3) the problem of answering queries in deductive databases with limited use of successor functions. As a consequence, we settle an open problem concerning lower bounds for the PFD logical implication problem and show that a regularity condition for DLClass that ensures low order polynomial time decidability for its logical implication problem is tight.

[1]  J. Lloyd.  Foundations of Logic Programming , 1984, Symbolic Computation.

[2]  J. W. Lloyd,et al.  Foundations of logic programming; (2nd extended ed.) , 1987 .

[3]  Deborah L. McGuinness,et al.  CLASSIC: a structural data model for objects , 1989, SIGMOD '89.

[4]  Grant E. Weddell,et al.  A Theory of Functional Dependencies for Object-Oriented Data Models , 1989, DOOD.

[5]  Jan Chomicki,et al.  Functional deductive databases: query processing in the presence of limited function symbols , 1990 .

[6]  Grant E. Weddell,et al.  Reasoning about functional dependencies generalized for semantic data models , 1992, TODS.

[7]  Jan Chomicki,et al.  Finite representation of infinite query answers , 1993, TODS.

[8]  Grant E. Weddell,et al.  Reasoning About Equations and Functional Dependencies on Complex Objects , 1994, IEEE Trans. Knowl. Data Eng..

[9]  Minoru Ito,et al.  Implication Problems for Functional Constraints on Databases Supporting Complex Objects , 1994, J. Comput. Syst. Sci..

[10]  Diego Calvanese,et al.  Structured Objects: Modeling and Reasoning , 1995, DOOD.

[11]  Alexander Borgida,et al.  Description Logics in Data Management , 1995, IEEE Trans. Knowl. Data Eng..

[12]  Alexander Borgida,et al.  Adding Uniqueness Constraints to Description Logics (Preliminary Report) , 1997, DOOD.

[13]  Wenfei Fan,et al.  Path constraints on semistructured and structured data , 1998, PODS '98.

[14]  Diego Calvanese,et al.  Description Logics for Conceptual Data Modeling , 1998, Logics for Databases and Information Systems.

[15]  Peter Buneman,et al.  Path Constraints in Semistructured and Structured Databases. , 1998, PODS 1998.

[16]  Wenfei Fan,et al.  Interaction between path and type constraints , 1999, PODS '99.

[17]  Diego Calvanese,et al.  Answering Queries Using Views in Description Logics , 1999, KRDB.

[18]  Vitaliy L. Khizder,et al.  Reasoning about Duplicate Elimination with Description Logic , 2000, Computational Logic.

[19]  Vitaliy L. Khizder,et al.  Uniqueness constraints in object-relational databases and description logics , 2000 .

[20]  Wenfei Fan,et al.  Integrity constraints for XML , 2000, PODS '00.

[21]  Serge Abiteboul,et al.  Queries and computation on the web , 1997, Theor. Comput. Sci..

[22]  Diego Calvanese,et al.  Keys for Free in Description Logics , 2000, Description Logics.