## Foundations of canonical update support for closed database views (1990)

Venue: | ICDT’90, Third International Conference on Database Theory |

Citations: | 25 - 9 self |

### BibTeX

@INPROCEEDINGS{Hegner90foundationsof,

author = {Stephen J. Hegner},

title = {Foundations of canonical update support for closed database views},

booktitle = {ICDT’90, Third International Conference on Database Theory},

year = {1990},

pages = {422--436},

publisher = {Springer-Verlag}

}

### Years of Citing Articles

### OpenURL

### Abstract

A closed view of a database schema is one which is totally encapsulated. Insofar as the user is concerned, the view is the database schema. The rest of the database system is not visible through the view, and is is not required for complete use of the view. Similarly, the updates which may be effected through the view have their scope limited entirely to that view. In this paper, we lay the mathematical foundations for the systematic support of such views. The proper context is shown to be that of update translation under constant meet complement, a refinement of the constant complement strategy of Bancilhon and Spyratos. The central complexity result for relational schemata is that checking the legality of updates is “infinitely ” simpler than blindly checking that the new state is legal for the view schema, and in the particular case that the base schema is constrained by functional dependencies, may always be performed in constant time, even if the view schema is not finitely axiomatizable. We further establish that, under very natural assumptions, update strategies for closed views are unique.

### Citations

598 |
A Mathematical Introduction to Logic
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- 2002
(Show Context)
Citation Context ...ional notation and terminology of the relational model, as may be found in [Mai83] and [PDGV89]. For Sections 3 and 4, we also assume some basic familiarity with first-order logic, as may be found in =-=[End72]-=- or [Gal86]. 2sDue to space limitations, it has been necessary to omit many details and essentially all proofs. Complete reports containing a more detailed development, including proofs, will be avail... |

448 |
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(Show Context)
Citation Context ..., 1 ≤ i ≤ Ar(R), occurs in some αi. (Recall that the full definition of R is R(v1, . . . , v Ar(R)) ⇔ Def(γ, R).) Our ∃+∧-views are essentially the so-called conjunctive queries of Chandra and Merlin =-=[CM76]-=-. Note that any composition of the projection, restriction, and join operators yields an ∃+∧-view. We say that two relational views Γ1 and Γ2 are ∃+∧-isomorphic, and write Γ1 ∼ =[∃+∧] Γ2, if they are ... |

431 |
The Theory of Relational Databases
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(Show Context)
Citation Context ...tions, relative to the current thrust of the general theory of database updates. We assume familiarity with the by now traditional notation and terminology of the relational model, as may be found in =-=[Mai83]-=- and [PDGV89]. For Sections 3 and 4, we also assume some basic familiarity with first-order logic, as may be found in [End72] or [Gal86]. 2sDue to space limitations, it has been necessary to omit many... |

187 | Update Semantics of Relational Views
- Bancilhon, Spyratos
(Show Context)
Citation Context ...pair Γ = (V, γ) in which V is a set-based database schema and γ : D → V is a set-based morphism with the property that γ ′ : LDB(D) → LDB(V) is surjective. The congruence Congr(Γ) of Γ (denoted ≡Γ in =-=[BS81b]-=-) is the equivalence relation on LDB(D) defined by (M1, M2) ∈ Congr(Γ) iff γ ′ (M1) = γ ′ (M2). Given set-based views Γ1 = (V1, γ1) and Γ2 = (V2, γ2), a view morphism f : Γ1 → Γ2 is a set-based databa... |

71 |
Properties and update semantics of consistent views
- Gottlob, Paolini, et al.
- 1988
(Show Context)
Citation Context ...degree, is that based upon the constantcomplement strategy of Bancilhon and Spyratos [BS81b, BS81a]. This includes subsequent work by Cosmadakis and Papadimitriou [CP84], Gottlob, Paolini, and Zicari =-=[GPZ88]-=-, and our own earlier work [Heg84]. Because we start by postulating properties of an update strategy rather than by fixing a strategy itself, our approach does not presuppose constantcomplement update... |

61 |
Updates, a new frontier
- Abiteboul
- 1988
(Show Context)
Citation Context ...ing his stay there.s0. Introduction The capability to perform updates has always been an integral part of database systems, although only recently has the problem begun to be addressed systematically =-=[Abi88]-=-. The ability to perform updates through views — windows on the database which allow only partial access — is also a useful service of a complete database system. It is the stated goal of this researc... |

60 |
Procedural languages for database queries and updates
- Abiteboul, Vianu
- 1990
(Show Context)
Citation Context ...reversible (symmetry of UD.) Of course, in current research in the study of database transactions, the set UD is specified by some sort of transaction language, such as TL, detTL, and their relatives =-=[AV90]-=-. However, at this point, it would not serve our purpose to incorporate such a language into our model, since we are interested in general admissibility of updates, irrespective of the characteristics... |

60 | Horn clauses and database dependencies
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- 1982
(Show Context)
Citation Context ...re able to establish some very strong results. 3.8 Notation and the context We now let D be the schema whose single relation symbol is R[U]. Recall that an typed equality generating dependency (TEGD) =-=[Fag82]-=- (also 12scalled a generalized functional dependency [Mai83, 14.7], [FV86]) is a sentence of the form m� ( R(xi1, . . . , xin)) ⇒ (xjℓ = xkℓ ) i=1 On the left-hand side, some of the xα’s may be the sa... |

60 |
Algorithms for translating view updates to database updates for views involving selections, projections, and joins
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- 1985
(Show Context)
Citation Context ...upported by a sort of “toolkit” which the user may employ to construct and customize a view, and much of the work identified above could well provide the foundation for such a package. Indeed, Keller =-=[Kel85]-=- has already made a proposal for such a package, and Medieros and Tompa [MT85] have implemented a package to understand various update policies. In contrast to such a “toolkit” approach for open views... |

57 |
Updates of relational views
- Cosmadakis, Papadimitriou
- 1984
(Show Context)
Citation Context ...rt in closed views, at least to some degree, is that based upon the constantcomplement strategy of Bancilhon and Spyratos [BS81b, BS81a]. This includes subsequent work by Cosmadakis and Papadimitriou =-=[CP84]-=-, Gottlob, Paolini, and Zicari [GPZ88], and our own earlier work [Heg84]. Because we start by postulating properties of an update strategy rather than by fixing a strategy itself, our approach does no... |

47 |
Logic for computer science
- Gallier
- 1987
(Show Context)
Citation Context ...ion and terminology of the relational model, as may be found in [Mai83] and [PDGV89]. For Sections 3 and 4, we also assume some basic familiarity with first-order logic, as may be found in [End72] or =-=[Gal86]-=-. 2sDue to space limitations, it has been necessary to omit many details and essentially all proofs. Complete reports containing a more detailed development, including proofs, will be available. 1. Se... |

36 | On the updatability of relational views - Dayal, Bernstein - 1978 |

30 |
The theory of data dependencies - a survey
- Fagin, Vardi
- 1986
(Show Context)
Citation Context ... We now let D be the schema whose single relation symbol is R[U]. Recall that an typed equality generating dependency (TEGD) [Fag82] (also 12scalled a generalized functional dependency [Mai83, 14.7], =-=[FV86]-=-) is a sentence of the form m� ( R(xi1, . . . , xin)) ⇒ (xjℓ = xkℓ ) i=1 On the left-hand side, some of the xα’s may be the same, provided they are in the same column of R. A functional dependency (FD... |

28 | Choosing a view update translator by dialog at view definition time - Keller - 1986 |

28 |
The Structure of the Relational Database Model
- Paredaens, Bra, et al.
- 1989
(Show Context)
Citation Context ...ive to the current thrust of the general theory of database updates. We assume familiarity with the by now traditional notation and terminology of the relational model, as may be found in [Mai83] and =-=[PDGV89]-=-. For Sections 3 and 4, we also assume some basic familiarity with first-order logic, as may be found in [End72] or [Gal86]. 2sDue to space limitations, it has been necessary to omit many details and ... |

21 | Updates to Relational Database Through Views Involving Joins - Keller - 1982 |

19 |
A relational database view update translation mechanism
- Masunaga
- 1984
(Show Context)
Citation Context ... DB82] and Furtado et al [FSdS79]. Perhaps the most visible proponent of update strategies for open views has been Keller [Kel82, Kel85, Kel84, Kel87]. Other work along these lines include [MT85] and =-=[Mas84]-=-. Generally, these works look at “most plausible” strategies for restricted cases, such as updating projections or join of relations governed by functional dependencies. The resulting updates typicall... |

17 |
Understanding the implications of view update policies
- Medeiros, Tompa
- 1985
(Show Context)
Citation Context ...tein [DB78, DB82] and Furtado et al [FSdS79]. Perhaps the most visible proponent of update strategies for open views has been Keller [Kel82, Kel85, Kel84, Kel87]. Other work along these lines include =-=[MT85]-=- and [Mas84]. Generally, these works look at “most plausible” strategies for restricted cases, such as updating projections or join of relations governed by functional dependencies. The resulting upda... |

14 | Unique complements and decompositions of database schemata
- Hegner
- 1994
(Show Context)
Citation Context ... complements of one another. If the decomposition map is furthermore bijective, the pair {Γ1, Γ2} is called a direct complementary pair, and Γ1 and Γ2 are called direct complements of one another. In =-=[Heg89]-=-, we have investigated extensively the properties of direct complementary pairs, and, more generally, direct decompositions into any number of finite components. Such 4sdecompositions are the natural ... |

11 | A Transaction{Based Approach to Relational Database Speci - Abiteboul, Vianu - 1989 |

9 |
Preserving Functional Dependencies
- Beeri, Honeyman
- 1981
(Show Context)
Citation Context ...d cover of Ψ into {U1, U2} is a set Φ of TEGD’s on R[U] such that Mod(Ψ) = Mod(Φ) and each ϕ ∈ Φ embeds in either U1 or U2. Clearly, this generalizes the notion of an embedded cover for a set of FD’s =-=[BH81]-=-. 3.9 Lemma Let D be the single relation schema R[U], constrained by a set of TEGD’s plus a single join dependency ✶ [U1, U2]. Let Z be a subset of either U1 or else of U2. Then there is a (possibly i... |

8 |
Independent components of databases
- Bancilhon, Spyratos
- 1981
(Show Context)
Citation Context ... database context, Bancilhon and Spyratos addressed the issue of determining the conditions under which update admissibility is independent of the complement state in their VLDB paper on independence =-=[BS81a]-=-. While their presentation is sketchy, they do recapture some of the ideas we have presented here with their notion of weak independence. However, they seem to have been unaware of the commuting congr... |

8 |
On interpretations of relational languages and solutions to the implied constraint problem
- Jacobs, Aronson, et al.
- 1982
(Show Context)
Citation Context ...y convention) exactly the variables in {v1, . . . v Ar(R)} free. The instance of R defined by the formula (or query) R(v1, . . . , v Ar(R)) ⇔ Def(γ, R), gives rise to γ ′ in the natural fashion. (See =-=[JAK82]-=- for more on this idea.) In general, given a function γ ′ : LDB(D) → LDB(V), there are many different choices of {Def(γ, R) | R ∈ Rel(D)} which define it. We call such representations equivalent. Beca... |

7 |
Canonical view update support through Boolean algebra of components
- Hegner
- 1984
(Show Context)
Citation Context ...stantcomplement strategy of Bancilhon and Spyratos [BS81b, BS81a]. This includes subsequent work by Cosmadakis and Papadimitriou [CP84], Gottlob, Paolini, and Zicari [GPZ88], and our own earlier work =-=[Heg84]-=-. Because we start by postulating properties of an update strategy rather than by fixing a strategy itself, our approach does not presuppose constantcomplement update as a goal unto itself. However, w... |

6 | Comments on Bancilhon and Spyratos’ ‘Update semantics and relational views - Keller - 1987 |

4 |
A note on subdirect products
- Fleischer
- 1955
(Show Context)
Citation Context ...eep Γ constant. ✷ 2.11 Remarks on the literature Work on the problem of characterizing meet-like conditions in terms of commuting congruences in the setting of universal algebra goes back to at least =-=[Fle55]-=-. In the database context, Bancilhon and Spyratos addressed the issue of determining the conditions under which update admissibility is independent of the complement state in their VLDB paper on indep... |

3 |
Permitting updates through views of databases
- Furtado, Sevcik, et al.
- 1979
(Show Context)
Citation Context ...f supporting view updates is oriented towards the support of open views. The earliest efforts to systematically address the problem included that of Dayal and Bernstein [DB78, DB82] and Furtado et al =-=[FSdS79]-=-. Perhaps the most visible proponent of update strategies for open views has been Keller [Kel82, Kel85, Kel84, Kel87]. Other work along these lines include [MT85] and [Mas84]. Generally, these works l... |

3 |
Constant time maintenance or the triumph of fd's
- Graham, Wang
- 1986
(Show Context)
Citation Context ...the algorithm for (a). For (b), we note that it suffices to check the validity of the updates against a set of FD’s. This can be performed in time proportional to the size of the update, as argued in =-=[GW86]-=-. ✷ Let us remark in particular that in the case that we have an associative memory for the database which can do partial match retrieval of a single tuple in constant time (in the sense of [GW86]), t... |

1 | On the correct translation of update opeartions on relational views - Dayal, Bernstein |