## An order-based theory of updates for closed database views (2004)

### Cached

### Download Links

- [www.cs.umu.se]
- [www8.cs.umu.se]
- [www.cs.umu.se]
- DBLP

### Other Repositories/Bibliography

Venue: | Summary in /emphFoundations of Information and Knowledge Systems, Second International Symposium, 2002 |

Citations: | 17 - 8 self |

### BibTeX

@TECHREPORT{Hegner04anorder-based,

author = {Stephen J. Hegner},

title = {An order-based theory of updates for closed database views},

institution = {Summary in /emphFoundations of Information and Knowledge Systems, Second International Symposium, 2002},

year = {2004}

}

### Years of Citing Articles

### OpenURL

### Abstract

The fundamental problem in the design of update strategies for views of database schemata is that of selecting how the view update is to be reflected back to the base schema. This work presents a solution to this problem, based upon the dual philosophies of closed update strategies and order-based database mappings. A closed update strategy is one in which the entire set of updates exhibit natural closure properties, including transitivity and reversibility. The order-based paradigm is a natural one; most database formalisms endow the database states with a natural order structure, under which update by insertion is an increasing operation, and update by deletion is decreasing. Upon augmenting the original constant-complement strategy of Bancilhon and Spyratos – which is an early version of a closed update strategy – with compatible order-based notions, the reflection to the base schema of any update to the view schema which is an insertion, a deletion, or a modification which is realizable as a sequence of insertions and deletions is shown to be unique and independent of the choice of complement. In addition to this uniqueness characterization, the paper also develops a theory which identifies conditions under which a natural, maximal, update strategy exists for a view. This theory is then applied to a ubiquitous example – single-relational schemata constrained by equality-generating dependencies. Within this framework it is shown that for a view defined as a projection of the main relation, the only possibility is that the complement defining the update process is also a projection, and that the reconstruction is based upon functional dependencies. † A preliminary version of parts of this paper appeared as reference [16]. 1 1.

### Citations

1065 |
Introduction to Lattices and Order
- Davey, Priestley
- 2002
(Show Context)
Citation Context ... extensive use of terminology and results from order theory. Although some essential results are summarized in 2.1, a more general conceptual knowledge is expected. A good reference in this regard is =-=[6]-=-. At a more fundamental level, sequences of items will often be surrounded by angle brackets; e.g., 〈a, b, c, d, e〉. In that case, for a sequence σ, First(σ) is the first element of σ, and Last(σ) the... |

187 | Update Semantics of Relational Views
- Bancilhon, Spyratos
(Show Context)
Citation Context .... Fortunately, to a large degree, this has already been done. The seminal work on closed strategies is the constant-complement approach, developed more than twenty years ago by Bancilhon and Spyratos =-=[3]-=-. The idea is quite simple. To support updates to the view Γ of the main schema D, a view Γ ′ which is complementary to Γ is identified; i.e., {Γ, Γ ′ } forms a lossless decomposition of D. Then, the ... |

71 |
Properties and update semantics of consistent views
- Gottlob, Paolini, et al.
- 1988
(Show Context)
Citation Context ...N2) is well defined and well behaved, even if this update is not reversible. The idea of generalized deletions is closely related to the notion of updates with decreasing complements, in the sense of =-=[9]-=-, although here it is used as a tool to characterize views which admit update strategies in the sense of 3.1, rather than as a liberal form of update to be allowed on its own merits. 5.26 Examples — d... |

60 | Horn clauses and database dependencies - Fagin - 1982 |

45 | Entity-relationship modeling
- Thalheim
- 2000
(Show Context)
Citation Context ...st view updates can be accommodated within the constant-complement strategy. The most natural framework in which to pursue these ideas would be within HERM, the Higher-order Entity-Relationship Model =-=[20]-=-; conclusions about many modern data models could be extracted from a study based upon it. 56s8. Notes Added to the Revised Version A number of corrections have been made in this on-line version, part... |

25 | Foundations of canonical update support for closed database views
- Hegner
- 1990
(Show Context)
Citation Context ...cceptable according to certain criteria. The manner in which such suitability criteria are determined is one for which a variety of philosophies have emerged. 1.1 Open vs. closed update strategies In =-=[12]-=-, the extremes of suitability criteria for view updates have been termed open and closed update strategies. Roughly speaking, an open strategy is very liberal; as many updates as possible are allowed,... |

24 | A survey of current methods for integrity constraint maintenance and view updating
- Mayol, Teniente
- 1999
(Show Context)
Citation Context ...gle structure, rather than as a set of constraints, so applicability to deductive models is not clear. In any case, research on updates to deductive databases has taken a direction quite its own; see =-=[18]-=- for a recent survey. As mentioned in 1.4, the choice of order as a tool to establish uniqueness results is motivated by earlier work [15], in which such tools were used to show that decompositions in... |

14 | Unique complements and decompositions of database schemata
- Hegner
- 1994
(Show Context)
Citation Context ...h the “bad” views ΠT and Π ′ BC are not. Thus, these undesirable views may be excluded if attention is restricted to views whose underlying mappings are monotonic. The example schema E0 is taken from =-=[15]-=-, in which a study of unique decompositions was made. In that paper, it was shown that ΠS is the only complement of ΠR which is monotonic. However, the results of [15] are restricted to direct complem... |

12 |
Horizontal decompositions for handling exceptions to functional dependencies
- Bra, Paredaens
- 1983
(Show Context)
Citation Context ...nd b ∈ πB(N \ {(a, b)}). There is a simple way to view this family of updates. Perform a horizontal decomposition of the states N of R[AB] relative to the functional dependency A → B, in the sense of =-=[7]-=-. One component contains the largest subset N2 of N which satisfy the afunctional dependency A� �→ B, in the sense that for every (a, b) ∈ N2, there is another tuple (a, b ′ ) ∈ N2 with b �= b ′ . The... |

10 | Characterization of desirable properties of general database decompositions
- Hegner
(Show Context)
Citation Context ...ΠBC. This notion of the common component of two views is extremely important in a number of contexts involving views and database decomposition, including the generalization of acyclic decompositions =-=[14]-=- and decomposition into independent components [15]. Not surprisingly, it is also central to the constant complement strategy. For it to be well defined, the congruences of the two views must commute;... |

9 |
On the family of generalized dependency constraints
- Grant, Jacobs
- 1982
(Show Context)
Citation Context ...ecidable for replacing variables with constants in this way [1, Chap. 10]. For a firm mathematical foundation of how this method is tied to the resolution proof method and more traditional logic, see =-=[10]-=-. In this section, the notation Φ ⊢ ε will be used to denote that the equality term ε follows from Φ using the chase inference method. The soundness and completeness of this method ensures that this i... |

7 | View updates translations in relational databases
- Bentayeb, Laurent
(Show Context)
Citation Context ...s to the view update problem Over the years, there has been a substantial amount of research on the topic of view updates, a majority of which has focused upon the relational model; some quite recent =-=[5]-=-. The problem has also been studied, to a limited extent, in the context of the ER model [20, Sec. 8.3] and the object-oriented model [4]. However, except for the seminal work of Bancilhon and Spyrato... |

6 | Finitely specifiable implicational dependency families - Hull - 1984 |

5 | Uniqueness of update strategies for database views,” in
- Hegner
(Show Context)
Citation Context ... the reflection of order-based updates is unique in a strong and global sense. The proof offered in 4.2 and 4.3 below is a substantial simplification over that given in the earlier conference version =-=[16]-=-. 4.2 Lemma — characterization of formal insertions and deletions Let D be a database schema, let Γ = (V, γ) be a view of D, and let U and T be closed update families for D and V, respectively. Let ρ ... |

4 |
Some open problems on view axiomatization
- Hegner
- 1990
(Show Context)
Citation Context ... M2 ∈ LDBΦ(U), then M1, M2 ∈ LDB(U). Proof: For (a), consult [8, 6.1]. For an example of a schema constrained by functional dependencies whose projection is an infinite set of EGD’s, see [17, 4.1] or =-=[13]-=-. For (b), note that EGD’s can only constrain existing tuples; they have no capacity to generate new ones. Therefore, removing tuples cannot lead to a structure which does not satisfy an EGD satisfied... |

4 |
Constant-time maintainability: A generalization of independence
- Wang, Graham
- 1992
(Show Context)
Citation Context ...at under certain key situations, the reconstruction dependencies are functional dependencies. In view of the known results on constant-time updates for schemata constrained by functional dependencies =-=[21]-=-, this means that the complexity of a view update is no more than the complexity of the corresponding update in the main schema. However, for more general settings, additional investigations are in or... |

3 | Updates and object-generating views in ODBS - Bellahsène |

1 | Foundations of canonical update support for closed database views - Gratzer, Algebra, et al. - 1968 |

1 |
20] B. Thalheim, Entity-Relationship Modeling
- Monk, Logic, et al.
- 1976
(Show Context)
Citation Context ...e notation and representational techniques which are specific to the framework used in this paper. The following summary is present in that capacity. For further information on concepts within logic, =-=[19]-=- is a comprehensive reference. 6.2 The logic of a single-relation schema The logic LU of U has a sort \Sigma A for each A 2 U, and a single U-ary relation symbol, denoted by RU . For each A 2 U, it al... |