On the formal properties of transitive inheritance in databases

doi:10.1016/0020-0255(92)90088-P

Information Sciences

Volume 66, Issues 1–2, 1 December 1992, Pages 63-90

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Abstract

The paper investigates transitive inheritance relationships, represented formally by transitive inheritance dependencies (TIDs), between (sequences of) attributes of a relational scheme, e.g., part and subpart. The study of TIDs reveals a simple complete axiomatization for the implication problem, which is shown to be NP-complete. The interaction of TIDs with functional dependencies (FDs) is investigated, leading to the following main results: TIDs and FDs considered together imply new TIDs, but no new FDs. Furthermore, only longer TIDs, i.e., TIDs that contain more attributes, but not shorter ones, are implied. The membership problem for TIDs and FDs is decidable although the implication problem for FDs and TIDs together has no k-ary axiomatization. Sound and complete decision procedures are given for the membership problem for TIDs alone as well as for TIDs and FDs.

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Cited by (1)

Selective inheritance of attribute values in relational databases
1992, Discrete Applied Mathematics
Selective inheritance dependencies, or SIDs, are introduced to capture formally the inheritance of attribute values between tuples of any relation over a given relation scheme. It is shown that the membership problem, i.e., the question whether a SID is implied by a set of other SIDs, is NP-complete. Furthermore, a complete axiomatization for the implication problem of SIDs is given. Then, SIDs and functional dependencies (FDs) are studied together. SIDs and FDs together imply no other FDs than those already implied by the FDs alone. Although simple axiomatizations exist for FDs and SIDs separately, no k-ary axiomatization, i.e., no axiomatization in which every rule is k-ary for some fixed k, can fully describe the interaction between FDs and SIDs.

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Information Sciences

On the formal properties of transitive inheritance in databases

Abstract

Inclusion dependencies and their interaction with functional dependencies

J. Comput. Syst. Sci.

The theory of joins in relational databases

ACM Trans. Database Syst.

On the epistemological status of semantic networks

The implication problem for functional and inclusion dependencies is undecidable

SIAM J. Comput.

Decomposition of a data base and the theory of boolean switching functions

IBM J. Res. Dev.

Multivalued dependencies and a new normal form for relational databases

ACM Trans. Database Syst.

Computers and Intractability

Selective inheritance of attribute values in relational databases