## Justification for inclusion dependency normal form (2000)

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Venue: | IEEE Transactions on Knowledge and Data Engineering |

Citations: | 24 - 6 self |

### BibTeX

@ARTICLE{Levene00justificationfor,

author = {Mark Levene and Millist W. Vincent},

title = {Justification for inclusion dependency normal form},

journal = {IEEE Transactions on Knowledge and Data Engineering},

year = {2000},

volume = {12},

pages = {2000}

}

### Years of Citing Articles

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### Abstract

permission from the publisher. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. © 2000 IEEE. Copyright and all rights therein are retained by authors or by other copyright holders. All persons downloading this information are expected to adhere to the terms and constraints invoked by copyright. This document or any part thereof may not be reposted without the explicit permission of the copyright holder. Citation for this copy: Levene, Mark and Vincent, Millist W. (2000) Justification for inclusion dependency normal form. London: Birkbeck ePrints. Available at:

### Citations

1091 |
Principles of database and knowledge-base systems
- Ullman
- 1988
(Show Context)
Citation Context ...then it is not in VRFNF. This result follows because if R is not in BCNF then there exists a non-trivial implied FD X ! A where X is not a superkey and using a well known construction (Theorem 7.1 in =-=[Ull88]-=-) there exists a two tuple relation r in which the tuples are identical on XA. The relation r is not in VRFNF since changing either of the A-values results in X ! A being violated. The only if part fo... |

450 |
The Theory of Relational Databases
- Maier
- 1983
(Show Context)
Citation Context ...IDNF is both a necessary and sufficient condition. Index TermsÐRelational database design, normal forms, functional dependency, inclusion dependency. 1 INTRODUCTION FUNCTIONAL dependencies (FDs) [2], =-=[25]-=-, [31], [1] generalize the notions of entity integrity and keys [13] and inclusion dependencies (INDs) [27], [8] generalize the notions of referential integrity and foreign keys [13], [17]. In this se... |

261 | Extending the database relational model to capture more meaning
- Codd
- 1979
(Show Context)
Citation Context ...ional database design, normal forms, functional dependency, inclusion dependency. 1 INTRODUCTION FUNCTIONAL dependencies (FDs) [2], [25], [31], [1] generalize the notions of entity integrity and keys =-=[13]-=- and inclusion dependencies (INDs) [27], [8] generalize the notions of referential integrity and foreign keys [13], [17]. In this sense, FDs and INDs are the most fundamental data dependencies that ar... |

242 |
Principles of Database and
- Ullman
- 1989
(Show Context)
Citation Context ...s both a necessary and sufficient condition. Index TermsÐRelational database design, normal forms, functional dependency, inclusion dependency. 1 INTRODUCTION FUNCTIONAL dependencies (FDs) [2], [25], =-=[31]-=-, [1] generalize the notions of entity integrity and keys [13] and inclusion dependencies (INDs) [27], [8] generalize the notions of referential integrity and foreign keys [13], [17]. In this sense, F... |

174 |
On the desirability of acyclic database schemes
- Beeri, Fagin, et al.
- 1983
(Show Context)
Citation Context ...are consistent if the set of INDs I includes the two INDs: R[R " S] ` S[R " S] and S[R " S] ` R[R " S]. A database schema R is pairwise consistent if every pair of its relation sch=-=emas are consistent [BFMY83]-=-; we note that pairwise consistency can be expressed by a set of proper circular INDs.) In this case we need alternative semantics to express the goal of normalisation. A minimal requirement is that t... |

128 | Multivalued dependencies and a new normal form for relational databases
- FAGIN
- 1977
(Show Context)
Citation Context ...hat X cannot be a superkey and, hence, that R is not in BCNF and, so, establishes the only if part. tu In [34], it was shown that, in the presence of multivalued dependencies, 4NF (fourth normal form =-=[18]-=-) is also equivalent to VRFNF. Somewhat surprisingly, the syntactic equivalent for VRFNF in the most general case, where join dependencies are present, is a new normal form that is weaker than PJ/NF (... |

118 |
Computational problems related to the design of normal form relational schemes
- BEERI, BERNSTEIN
- 1979
(Show Context)
Citation Context ...undamental data dependencies that arise in practice. Relational database design in the presence of FDs is an established area in database theory which has been researched for more than 20 years [12], =-=[3]-=-, [25], [31], [1]. The semantic justification of the normal forms in the presence of FDs is well-understood in terms of eliminating the so-called update anomalies and redundancy problems that can aris... |

115 |
Testing containment of conjunctive queries under functional and inclusion dependencies
- Johnson, Klug
- 1984
(Show Context)
Citation Context ... state of d.s284 IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING, VOL. 12, NO. 2, MARCH/APRIL 2000 We observe that if we allow I to be circular, then the chase procedure does not always terminate =-=[22]-=-. (When the chase of d with respect to does not terminate, then CHASE(d; ) is said to violate a set of FDs G over R, i.e., CHASE(d; ) 6ƒ G, if after some finite number of applications of the IND rule ... |

107 | Dependency structures of data base relationships - Armstrong - 1974 |

100 |
The Design of Relational Databases
- Mannila, Räihä
- 1994
(Show Context)
Citation Context ...ion is fundamental to the success of a design since the enforcement of referential integrity is no simple matter [14]. Normal forms which include FDs and INDs have been considered in [7], [28], [23], =-=[29]-=-, [4], but necessary and sufficient conditions in terms of remov. M. Levene is with the Department of Computer Science, University College London, Gower Street, London WC1E 6BT, UK. E-mail: mlevene@cs... |

92 |
Inclusion dependencies and their interaction with functional dependencies
- Casanova, Fagin, et al.
- 1984
(Show Context)
Citation Context ...al dependency, inclusion dependency. 1 INTRODUCTION FUNCTIONAL dependencies (FDs) [2], [25], [31], [1] generalize the notions of entity integrity and keys [13] and inclusion dependencies (INDs) [27], =-=[8]-=- generalize the notions of referential integrity and foreign keys [13], [17]. In this sense, FDs and INDs are the most fundamental data dependencies that arise in practice. Relational database design ... |

54 |
The Implication Problem for Functional and Inclusion Dependencies is Undecidable
- CHANDRA, VARDI
- 1983
(Show Context)
Citation Context ... [1] can be used to compute F ‡ and that Casanovas et al.'s axiom system [8] can be used to compute I ‡ . However, ‡ when we consider FDs and INDs together computing was shown to be undecidable [27], =-=[16]-=-. On the other hand, when I is noncircular, then Mitchell's axiom system [27] can be used to compute ‡ [10]. Moreover, in the special case, when I is a set of unary INDs, then Cosmadakis's et al. axio... |

49 |
Polynomial-time implication problems for unary inclusion dependencies
- Cosmadakis, Kanellakis, et al.
- 1990
(Show Context)
Citation Context ...other hand, when I is noncircular, then Mitchell's axiom system [27] can be used to compute ‡ [10]. Moreover, in the special case, when I is a set of unary INDs, then Cosmadakis's et al. axiom system =-=[11]-=- can be used to compute ‡ . The implication problem is the problem of deciding whether 2 ‡ , where is an FD or IND and is a set of FDs and INDs. It is well-known that the implication problem for FDs o... |

48 |
Normal forms and relational database operators
- FAGIN
- 1979
(Show Context)
Citation Context ...RFNF. Somewhat surprisingly, the syntactic equivalent for VRFNF, in the most general case where join dependencies are present, is a new normal form that is weaker than PJ/NF (project-join normal form =-=[Fag79]-=-) and 5NF (fifth normal form [Mai83]) [Vin98]. The concept of value redundancy is of little use though, in evaluating database designs in the presence of INDs because of the following result. It demon... |

47 |
Relational Database Theory
- Atzeni, Antonellis
- 1995
(Show Context)
Citation Context ... a necessary and sufficient condition. Index TermsÐRelational database design, normal forms, functional dependency, inclusion dependency. 1 INTRODUCTION FUNCTIONAL dependencies (FDs) [2], [25], [31], =-=[1]-=- generalize the notions of entity integrity and keys [13] and inclusion dependencies (INDs) [27], [8] generalize the notions of referential integrity and foreign keys [13], [17]. In this sense, FDs an... |

43 | A normal form for relational databases that is based on domains and keys
- Fagin
- 1981
(Show Context)
Citation Context ... of the normal forms in the presence of FDs is well-understood in terms of eliminating the so-called update anomalies and redundancy problems that can arise in a relation satisfying a set of FDs [6], =-=[20]-=-, [9], [33], [34]. The advice that is given as a result of this investigation of the semantics of the normal forms is that, in order to eliminate the above-mentioned problems, we should design databas... |

38 |
Functional and inclusion dependencies: A graph theoretic approach
- Cosmadakis, Kanellakis
- 1986
(Show Context)
Citation Context ...owever, ‡ when we consider FDs and INDs together computing was shown to be undecidable [27], [16]. On the other hand, when I is noncircular, then Mitchell's axiom system [27] can be used to compute ‡ =-=[10]-=-. Moreover, in the special case, when I is a set of unary INDs, then Cosmadakis's et al. axiom system [11] can be used to compute ‡ . The implication problem is the problem of deciding whether 2 ‡ , w... |

37 |
Towards a Sound View Integration Methodology
- Casanova, Vidal
- 1983
(Show Context)
Citation Context ... implication problem for INDs is, in general, PSPACE-complete [CFP84]. The implication problem for noncircular INDs is NP-complete [Man84, CK86]. Typed INDs have a polynomial time implication problem =-=[CV83]-=-. Unary INDs have a linear time implication problem [CKV90]. When we consider FDs and INDs together the implication problem is undecidable, as mentioned above. The implication problem for FDs and nonc... |

35 |
Recent investigations in relational data base systems
- Codd
- 1974
(Show Context)
Citation Context ...sult of this investigation of the semantics of the normal forms is that in order to eliminate the above mentioned problems we should design database schemas which are in Boyce-Codd Normal Form (BCNF) =-=[Cod74]-=-. Despite the importance of INDs as integrity constraints little research has been carried out on how they should be integrated into the normalisation process of a relational database. Such an integra... |

35 | Referential integrity - Date - 1986 |

34 |
The implication problem for functional and inclusion dependencies
- Mitchell
- 1983
(Show Context)
Citation Context ...nctional dependency, inclusion dependency. 1 INTRODUCTION FUNCTIONAL dependencies (FDs) [2], [25], [31], [1] generalize the notions of entity integrity and keys [13] and inclusion dependencies (INDs) =-=[27]-=-, [8] generalize the notions of referential integrity and foreign keys [13], [17]. In this sense, FDs and INDs are the most fundamental data dependencies that arise in practice. Relational database de... |

24 | What does Boyce-Codd normal form do - BERNSTEIN, GOODMAN - 1980 |

9 | Logical database design with inclusion dependencies - Ling, Goh - 1992 |

9 | How to prevent interaction of functional and inclusion dependencies
- Levene, Loizou
- 1999
(Show Context)
Citation Context ... FDs ff over R, for all subsets G ` F, G [ I j= ff if and only if G j= ff, and 2) for all INDs fi over R, for all subsets J ` I, F [ J j= fi if and only if J j= fi. The following theorem is proven in =-=[LL95]-=- (see [MR92, Chapter 10]). 6 Theorem 3.1 If R is in BCNF with respect to a set of FDs F over R I is a proper circular set of of INDs over R and \Sigma = F [ I is reduced then F and I do not interact. ... |

8 | Enforcing Inclusion Dependencies and Referential Integrity
- Tucherman
- 1988
(Show Context)
Citation Context ...e integrated into the normalisation process of a relational database. Such an integration is fundamental to the success of a design, since the enforcement of referential integrity is no simple matter =-=[CTF88]-=-. Normal forms which include FDs and INDs have been considered in [CA84, MR86, LG92, MR92, BD93] but necessary and sufficient conditions in terms of removing the update anomalies and redundancy proble... |

7 | A Design Theory for Solving the Anomalies Problem - Chan - 1989 |

7 |
The semantic justification for normal forms in relational database design
- Vincent
- 1994
(Show Context)
Citation Context ...mal forms in the presence of FDs is well-understood in terms of eliminating the so-called update anomalies and redundancy problems that can arise in a relation satisfying a set of FDs [6], [20], [9], =-=[33]-=-, [34]. The advice that is given as a result of this investigation of the semantics of the normal forms is that, in order to eliminate the above-mentioned problems, we should design database schemas w... |

7 | Amarel de Sa, “Mapping Uninterpreted Schemes into Entity-Relationship Diagrams: Two Applications to Conceptual Schema Design,”IBM - Casanova, J - 1984 |

6 |
Objects in Relational Database Schemes with Functional, Inclusion and Exclusion Dependencies
- Biskup, Dublish
- 1993
(Show Context)
Citation Context ... fundamental to the success of a design since the enforcement of referential integrity is no simple matter [14]. Normal forms which include FDs and INDs have been considered in [7], [28], [23], [29], =-=[4]-=-, but necessary and sufficient conditions in terms of remov. M. Levene is with the Department of Computer Science, University College London, Gower Street, London WC1E 6BT, UK. E-mail: mlevene@cs.ucl.... |

6 | Redundancy elimination and a new normal form for relational database design - Vincent - 1998 |

6 |
Abstraction in query processing
- Imielinski
- 1991
(Show Context)
Citation Context ... such that I contains the INDs: R 1 [X 1 ] ` R 2 [Y 2 ], R 2 [X 2 ] ` R 3 [Y 3 ], : : :, Rm [Xm ] ` R 1 [Y 1 ]. A set of INDs I is noncircular if it is not circular. The class of proper circular INDs =-=[Imi91]-=- defined below includes the class of noncircular INDs as a special case. 4 Definition 2.8 (Proper circular sets of INDs) A set I of INDs over R is proper circular if it is either noncircular or whenev... |

6 | Inclusion dependencies in database design - Mannila, Raiha - 1986 |

3 |
Comparing the universal instance and relational data models
- Sciore
- 1986
(Show Context)
Citation Context ...in VRFNF with respect to F. So it remains to show that R is in ARFNF. In the proof we utilise a directed graph representation, G I = (N, E), of the set of INDs I, which is constructed as follows (see =-=[Sci86]-=-). Each relation schema R in R has a separate node in N labelled R; we do not distinguish between nodes and their labels. There is an arc (R, S) 2 E if and only if there is a nontrivial IND R[X] ` S[Y... |

2 |
On the desirability of acyclic database
- BEERI, FAGIN, et al.
- 1983
(Show Context)
Citation Context ...d S are consistent if the set of INDs I includes the two INDs: R[R \ S] S[R \ S] and S[R \ S] R[R \ S]. A database schema R is pairwise consistent if every pair of its relation schemas are consistent =-=[5]-=-; we note that pairwise consistency can be expressed by a set of proper circular INDs.) In this case, we need alternative semantics to express the goal of normalization. A minimal requirement is that ... |

2 | Modification anomalies and Boyce-Codd normal form - Vincent - 1992 |

1 | ªDependency Structures of Data Base Relationships,º - Armstrong - 1974 |

1 |
ªWhat Does Boyce-Codd Normal Form Do?º
- Bernstein, Goodman
- 1980
(Show Context)
Citation Context ...ation of the normal forms in the presence of FDs is well-understood in terms of eliminating the so-called update anomalies and redundancy problems that can arise in a relation satisfying a set of FDs =-=[6]-=-, [20], [9], [33], [34]. The advice that is given as a result of this investigation of the semantics of the normal forms is that, in order to eliminate the above-mentioned problems, we should design d... |

1 |
de Sa, ªMapping Uninterpreted Schemes into Entity-Relationship Diagrams: Two Applications to Conceptual Schema Design,º
- Casanova, Amaral
- 1984
(Show Context)
Citation Context ... Such an integration is fundamental to the success of a design since the enforcement of referential integrity is no simple matter [14]. Normal forms which include FDs and INDs have been considered in =-=[7]-=-, [28], [23], [29], [4], but necessary and sufficient conditions in terms of remov. M. Levene is with the Department of Computer Science, University College London, Gower Street, London WC1E 6BT, UK. ... |

1 |
ªEnforcing Inclusion Dependencies and
- Casanova, Tucherman, et al.
- 1988
(Show Context)
Citation Context ...be integrated into the normalization process of a relational database. Such an integration is fundamental to the success of a design since the enforcement of referential integrity is no simple matter =-=[14]-=-. Normal forms which include FDs and INDs have been considered in [7], [28], [23], [29], [4], but necessary and sufficient conditions in terms of remov. M. Levene is with the Department of Computer Sc... |

1 |
ªTowards a Sound View Integration Methodology,º
- Casanova, Vidal
- 1983
(Show Context)
Citation Context ...nd, the implication problem for INDs is, in general, PSPACE-complete [8]. The implication problem for noncircular INDs is NP-complete [26], [10]. Typed INDs have a polynomial time implication problem =-=[15]-=-. Unary INDs have a linear time implication problem [11]. When we consider FDs and INDs together, the implication problem is undecidable, as mentioned above. The implication problem for FDs and noncir... |

1 |
ªReferential Integrity,º Relational Database: Selected Writings
- Date
- 1986
(Show Context)
Citation Context ... (FDs) [2], [25], [31], [1] generalize the notions of entity integrity and keys [13] and inclusion dependencies (INDs) [27], [8] generalize the notions of referential integrity and foreign keys [13], =-=[17]-=-. In this sense, FDs and INDs are the most fundamental data dependencies that arise in practice. Relational database design in the presence of FDs is an established area in database theory which has b... |

1 |
ªNormal Forms and Relational Database Operators,º
- Fagin
- 1979
(Show Context)
Citation Context ...RFNF. Somewhat surprisingly, the syntactic equivalent for VRFNF in the most general case, where join dependencies are present, is a new normal form that is weaker than PJ/NF (project-join normal form =-=[19]-=-) and 5NF (fifth normal form [25]) [34]. The concept of value redundancy is of little use though in evaluating database designs in the presence of INDs because of the following result. It demonstrates... |

1 |
ªAbstraction in Query Processing,º
- Imielinski
- 1991
(Show Context)
Citation Context ... R1;R2;R3; ...;Rm 2 R, with m>1, such that I contains the INDs: R1‰X1Š R2‰Y2Š;R2‰X2Š R3‰Y3Š; ...;Rm‰XmŠ R1‰Y1Š: A set of INDs I is noncircular if it is not circular. The class of proper circular INDs =-=[21]-=- defined below includes the class of noncircular INDs as a special case. Definition 2.8 (Proper circular sets of INDs). A set I of INDs over R is proper circular if it is either noncircular or wheneve... |

1 |
ªLogical Database Design with Inclusion Dependencies,º
- Ling, Goh
- 1992
(Show Context)
Citation Context ...tegration is fundamental to the success of a design since the enforcement of referential integrity is no simple matter [14]. Normal forms which include FDs and INDs have been considered in [7], [28], =-=[23]-=-, [29], [4], but necessary and sufficient conditions in terms of remov. M. Levene is with the Department of Computer Science, University College London, Gower Street, London WC1E 6BT, UK. E-mail: mlev... |

1 |
ªHow to Prevent Interaction of Functional and
- Levene, Loizou
- 1995
(Show Context)
Citation Context ...s I over R if 1. for all FDs over R, for all subsets G F, G [ I ƒ if and only if G ƒ , and 2. for all INDs over R, for all subsets J I, F [ J ƒ if and only if J ƒ . The following theorem is proven in =-=[24]-=- (see [29, Chapter 10]). Theorem 3.1. If R is in BCNF with respect to a set of FDs F over R, I is a proper circular set of of INDs over R and ˆ F [ I is reduced, then F and I do not interact. As the n... |

1 | On the complexity of the inference problem for subclasses of inclusion dependencies - Mannila - 1984 |

1 |
ªInclusion Dependencies
- Mannila, RaÈihaÈ
- 1986
(Show Context)
Citation Context ... an integration is fundamental to the success of a design since the enforcement of referential integrity is no simple matter [14]. Normal forms which include FDs and INDs have been considered in [7], =-=[28]-=-, [23], [29], [4], but necessary and sufficient conditions in terms of remov. M. Levene is with the Department of Computer Science, University College London, Gower Street, London WC1E 6BT, UK. E-mail... |

1 |
The Economy Colombia is a traditionally well-diversified economy with an anmual GDP growth rate of around 5 percent until the first half of the 1980s, when the average growth fell to 2.1 percent Econoidc performance during the 1970s was satisfactory with
- unknown authors
- 1986
(Show Context)
Citation Context ...em results in Ri[X] Rj[Y] being violated. tu Due to the above lemma, we require only that the design be in VRFNF with respect to the FDs, but not with respect to the INDs. However, as noted by others =-=[30]-=-, [23], [29], an even stronger form of redundancy can occur in a database in the presence of INDs. We refer to this as attribute redundancy, which was illustrated in Example 1.1 given in the introduct... |

1 |
ene sector, electricity is of particular significance in this context This chapter examines the impact of electricity price changes during 1985-88. From 1979 to 1985, the energy sector absorbed neary half of all public invesent resources and two-thirds of
- unknown authors
- 1990
(Show Context)
Citation Context ...distinct from other types of update anomalies as investigated in [6], [33]). This concept was originally introduced in [20] to deal with the insertion and deletion of tuples and was later extended in =-=[32]-=-, [33] to include the modifications of tuples. A key-based update anomaly is defined to occur when an update to a relation, which can either be an insertion or a deletion or a modification, results in... |