## Databases and Finite-Model Theory (1997)

Venue: | IN DESCRIPTIVE COMPLEXITY AND FINITE MODELS |

Citations: | 6 - 0 self |

### BibTeX

@INPROCEEDINGS{Vianu97databasesand,

author = {Victor Vianu},

title = {Databases and Finite-Model Theory},

booktitle = {IN DESCRIPTIVE COMPLEXITY AND FINITE MODELS},

year = {1997},

pages = {97--148},

publisher = {American Mathematical Society}

}

### OpenURL

### Abstract

Databases provide one of the main concrete scenarios for finitemodel theory within computer science. This paper presents an informal overview of database theory aimed at finite-model theorists, emphasizing the specificity of the database area. It is argued that the area of databases is a rich source of questions and vitality for finite-model theory.

### Citations

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454 |
The Theory of Relational Databases
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(Show Context)
Citation Context ...flavor of the database area, and to incite curiosity. We refer the reader to [Kan91, AHV95] for more detailed and somewhat formal presentations of database theory. Early database theory is covered in =-=[Mai83]-=-. A concise overview of the field aimed at computer science theoreticians is also provided in [Yan95]. The relationship of database theory and practice is explored in [Pap95]. A general introduction t... |

358 | Combining Fuzzy Information from Multiple Systems - Fagin - 1996 |

354 | Constraint query languages
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Citation Context ...ea of spatial databases. These handle information about regions in space. Such information is conceptually infinite, but must be finitely represented. One solution is provided by constraint databases =-=[KKR90]-=-. These introduce an extension of the relational model where tuples are replaced by constraints over points in space, specified by boolean combinations of polynomial inequalities with integer coeffici... |

296 |
Object identity as a query language primitive
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(Show Context)
Citation Context ...lows for value creation and is complete in the classical sense, would also be complete in the extended sense. It turns out that this is not the case. This is illustrated by the following example from =-=[AK89]-=-. Consider a query whose input consists of a graph with vertices fa; bg and no edges, and whose output consists of a graph with vertices fa; bg, additional new vertices f/ 0 ; / 1 ; / 2 ; / 3 g, and w... |

280 |
The Classical Decision Problem
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(Show Context)
Citation Context ...r example, the class of sentences 26 VICTOR VIANU corresponding to fds+incds is not subsumed by any of the classes for which undecidability of finite implication has been known in finite-model theory =-=[BGG96]-=-; undecidability had to be proven from scratch. However, results and formalisms from finite-model theory are sometimes unexpectedly and beautifully reinforced by databases. From the apparent cacophony... |

275 | Relational queries computable in polynomial time - Immerman - 1986 |

248 | Structure and complexity of relational queries
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(Show Context)
Citation Context ...emerges very naturally in the context of the data independence principle. 4.4. Complete languages. A query language is said to be complete if it expresses precisely the computable and generic queries =-=[CH80a]-=-. The quest for a complete query language was an early preoccupation in database theory. Note that all query languages we have considered so far have complexity within PSPACE. The most powerful of the... |

216 | The alternating fixpoint of logic programs with negation - GELDER - 1989 |

209 | Principles of Database and Knowledge Base Systems - Ullman - 1989 |

207 |
Universality of data retrieval languages
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(Show Context)
Citation Context ... particular allegiance to logic! The inability of FO to express certain useful queries, such as connectivity of finite graphs, was noted early on by database theoreticians ([Fag75], and independentlys=-=[AU79]-=-). Such facts have led to the introduction of a variety of extensions of FO with recursion. Some of the proposed paradigms are illustrated next. ffl Logic: Extensions of FO with logical flavor include... |

205 | Efficiently updating materialized views - Blakeley, Larson, et al. - 1986 |

198 | Update semantics of relational views
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Citation Context ...ward. The second school attempts to identify reasonable situations when the translation can be done automatically and unambiguously. This has given rise to an elegant theory which we briefly describe =-=[BS81]-=-. The main idea is to disambiguate updates to a given view v using a second view v 0 , called a complement of v. In order for v 0 to be a complement of v, the two views taken together must uniquely id... |

156 |
Datalog extensions for database queries and updates
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(Show Context)
Citation Context ...s that extend FO with recursion, such as Datalog (see [MW88]), the fixpoint queries (expressed by FO+LFP [CH82] and FO+IFP [GS86]) and the while queries 3 (expressed by FO+PFP, partial fixpoint logic =-=[AV91a]-=-). The connection between languages and complexity classes is of great interest to both fields. In particular, the existence of a language expressing precisely the queries in P remains the major open ... |

155 | Logic and the Challenge of Computer Science - Gurevich - 1988 |

153 | Data structures for on-line updating of minimum spanning trees, with applications - Frederickson - 1985 |

147 | Temporal and modal logic. In Handbook of theoretical computer science (vol. B): formal models and semantics - Emerson - 1990 |

143 | Every logic program has a natural stratification and an iterated least fixed point model - Przymusinski - 1989 |

138 | An optimal lower bound on the number of variables for graph identification - Cai, Furer, et al. - 1992 |

138 | Well-founded semantics coincides with three-valued stable-semantics, Fund - Przymusinski - 1990 |

132 | Negation as failure using tight derivations for general logic programs - Gelder - 1988 |

128 | Multivalued dependencies and a new normal form for relational databases
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(Show Context)
Citation Context ...s and the second are generalizations of fds. Several deep questions arose that remained open for some time, such as the decidability of implication for the class of embedded multi-valued dependencies =-=[Fag77]-=-. The question was recently settled in the negative [Her95]. Comprehensive presentations of dependency theory can be found in [Var87, FV86]. A more concise presentation is provided in [Kan91]. Depende... |

122 |
Generic computation and its complexity
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(Show Context)
Citation Context ...a at the physical level of a database. Thus, abstraction is absent. Relational machines. Computation without order is modeled by a device called a relational machine, operating directly on structures =-=[AV91b]-=-. (A closely related idea, of generalizing Turing machines to operate on general structures, goes back to [Fri71] and was investigated extensively in [Lei89a, Lei89b] for ordered structures. ) A relat... |

118 |
Computational problems related to the design of normal form relational schemes
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- 1979
(Show Context)
Citation Context ...ations and X is a set of attributes common to P and Q. The meaning is that ��X (P ) ` ��X (Q). It turns out that the implication problem for fds and incds taken separately is decidable in line=-=ar time [BB79]-=- and polynomial space [CFP84], respectively. (The problem is PSPACE-complete for incds [CFP84].) The implication problem becomes undecidable for fds and incds taken together [CV85, Mit83]. The proof u... |

116 |
Computable queries for relational data bases
- Chandra, Harel
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(Show Context)
Citation Context ...plex game trees [Kol91]. Occasionally, questions and results originating in database theory have contributed to finite-model theory. The very concept of query was first articulated in database theory =-=[CH80b]-=- (although this is closely related to generalized quantifiers) . The question of the recursive enumeration of the queries in P again originated in database theory [CH82]. As discussed in Section 4.3, ... |

116 | Testing implication of data dependencies
- Maier, Sagiv
- 1979
(Show Context)
Citation Context ... 0 ; b; ci in R. These agree on B. Since R satisfies B ! C, it must be that c = c 0 . But then ha; b; ci is in R. This kind of reasoning about fds and queries illustrates a technique called the chase =-=[MMS79]-=-. Much algorithmic and data structures work has gone into the design of indexes, such as B + -trees [BU77]. Roughly speaking, a B + -tree allows log(n)-time access to one of n records, if the tree is ... |

115 |
Testing containment of conjunctive queries under functional and inclusion dependencies
- Johnson, Klug
- 1984
(Show Context)
Citation Context ...del theory was first considered. It introduced the notion of finite implication (implication over finite structures) and contrasted it to unrestricted implication over arbitrary structures (e.g., see =-=[JK84]-=-). 1 The rationale for this difference with logic is simple enough: if the query asks for Joe's address, it actually means Joe and not Smith. Therefore there is no need to interpret Joe as anything bu... |

111 | Remark on the algebra of non first normal form relation - Jaeschke, Schek - 1982 |

109 | Temporal query languages: A survey
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(Show Context)
Citation Context ...ch issues have only recently begun to be explored [Cho92, LS87], and 10 VICTOR VIANU remain largely unresolved. A survey of temporal database research, emphasizing theoretical aspects, is provided in =-=[Cho94]-=-. 3.7. Below the Logical Level. While most database theory deals with the logical level, some of it concerns the levels below. This includes techniques for query processing, the design of physical acc... |

106 |
Further normalization of the data base relational model
- Codd
- 1972
(Show Context)
Citation Context ...r others. In the remainder of the section, the term "implication" means finite implication, unless otherwise stated. Two classes of dependencies have emerged as central: functional dependenc=-=ies (fds) [Cod72a]-=- and inclusion dependencies (incds) [Dat81]. We have seen informal examples of both in the previous section. Although inclusion dependencies often involve single attributes (as in the example), they g... |

104 |
A.: Cylindric algebras
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(Show Context)
Citation Context ...eturns all tuples t over att(R) [ att(S) such that �� att(R) (t) 2 R and �� att(S) (t) 2 S. The fact that FO has a simple algebraization had been known to logicians as Tarski's Algebraization =-=Theorem [HMT71]-=-. It was brought to the attention of the database community by Ted Codd [Cod70, Cod72b] (who went on to receive the Turing Award in 1981 for his development of the relational model [Cod87]). This resu... |

97 |
Pre b-trees
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(Show Context)
Citation Context ... in R. This kind of reasoning about fds and queries illustrates a technique called the chase [MMS79]. Much algorithmic and data structures work has gone into the design of indexes, such as B + -trees =-=[BU77]-=-. Roughly speaking, a B + -tree allows log(n)-time access to one of n records, if the tree is balanced. The main difficulty is how to efficiently keep the tree balanced as records are inserted or dele... |

92 |
Inclusion dependencies and their interaction with functional dependencies
- Casanova, Fagin, et al.
- 1984
(Show Context)
Citation Context ...ributes common to P and Q. The meaning is that ��X (P ) ` ��X (Q). It turns out that the implication problem for fds and incds taken separately is decidable in linear time [BB79] and polynomia=-=l space [CFP84]-=-, respectively. (The problem is PSPACE-complete for incds [CFP84].) The implication problem becomes undecidable for fds and incds taken together [CV85, Mit83]. The proof uses an elegant reduction of t... |

82 |
Fixed-point extensions of firstorder logic
- Gurevich, Shelah
- 1986
(Show Context)
Citation Context ...known to finite-model theorists. It consists of the investigation of languages that extend FO with recursion, such as Datalog (see [MW88]), the fixpoint queries (expressed by FO+LFP [CH82] and FO+IFP =-=[GS86]-=-) and the while queries 3 (expressed by FO+PFP, partial fixpoint logic [AV91a]). The connection between languages and complexity classes is of great interest to both fields. In particular, the existen... |

81 | Recursive unsolvability of a problem of Thue - POST - 1947 |

76 | Toward logic tailored for computational complexity - Gurevich - 1984 |

75 | Why not negation by fixpoint - Kolaitis, Papadimitriou - 1991 |

70 | Nested relational structures - Thomas, Fischer - 1986 |

68 | A consideration on normal form of not-necessarily-normalized relation in the relational data model
- Makinouchi
- 1977
(Show Context)
Citation Context ...sets. There are syntactic restrictions on the calculus and algebra that guarantee that all queries can be evaluated in polynomial-time. The earliest proposal to introduce complex values appears to be =-=[Mak77]-=-. Equivalent complex value calculus and algebra are proposed in [KV84, KV93, AB95]. Tractable restrictions are considered by many authors, including [JS82, TF86, RKS86, AB95, PG88, GV91]. Extended not... |

67 | Horn clauses and database dependencies - FAGIN - 1980 |

66 |
On Moschovakis closure ordinals
- Barwise
- 1977
(Show Context)
Citation Context ...e head to the right, and replace R 2 by R 2 " R 3 . Relational machines are closely related to a language very familiar to finitemodel theorists: infinitary logic with finitely many variables, L =-=! 1! [Bar77]-=-. It 4 Evenness is true iff the relation has an even number of elements. 5 Relational machines were initially called loosely coupled generic machines in [AV91b]. The term relational machine is used in... |

64 | General logical databases and programs: Default logic, semantics and stratification - Bidoit, Froidevaux - 1991 |

61 | Procedural and declarative database update languages (Extended Abstract - Abiteboul, Vianu - 1988 |

58 |
Procedural Languages for Database Queries and Updates
- Abiteboul, Vianu
(Show Context)
Citation Context ...he result of ' is added to the content of R. Noninflationary assignment, denoted R := ', is destructive: the old content of R not preserved. The language with inflationary semantics is called while + =-=[AV90]-=-, and the language with noninflationary semantics while [Cha81, CH82]. The followingswhile program computes the complement of the transitive closure of G: T := G; while change do begin T := fhx; yi j ... |