## Approximation in Databases (1995)

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Venue: | In PPCP'93, First International Workshop on Principles and Practice of Constraint Programming |

Citations: | 124 - 12 self |

### BibTeX

@INPROCEEDINGS{Libkin95approximationin,

author = {Leonid Libkin},

title = {Approximation in Databases},

booktitle = {In PPCP'93, First International Workshop on Principles and Practice of Constraint Programming},

year = {1995},

publisher = {Springer}

}

### Years of Citing Articles

### OpenURL

### Abstract

One source of partial information in databases is the need to combine information from several databases. Even if each database is complete for some "world", the combined databases will not be, and answers to queries against such combined databases can only be approximated. In this paper we describe various situations in which a precise answer cannot be obtained for a query asked against multiple databases. Based on an analysis of these situations, we propose a classification of constructs that can be used to model approximations. A major goal is to obtain universality properties for these models of approximations. Universality properties suggest syntax for languages with approximations based on the operations which are naturally associated with them. We prove universality properties for most of the approximation constructs. Then we use them to design languages built around datatypes given by the approximation constructs. A straightforward approach results in langauges that have a numb...

### Citations

337 | Constraint query languages - Kanellakis, Revesz - 1990 |

333 | Incomplete Information in Relational Databases - Imieliński, Lipski - 1984 |

253 | The Constraint Logic Programming Language CHIP - Dincbas, Hentenryck, et al. - 1988 |

144 | Semantics of Programming Languages - Gunter - 1992 |

142 | Equivalence of relational algebra and relational calculus query languages having aggregate functions - Klug - 1982 |

130 | Naturally embedded query languages - Tannen, Buneman, et al. - 1992 |

82 | On semantic issues connected with incomplete information databases - Lipski - 1979 |

75 | The DEDALE System for Complex Spatial Queries - GRUMBACH, RIGAUX, et al. |

64 | Using Powerdomains to Generalize Relational Databases - Buneman, Jung, et al. - 1991 |

60 | Database relations with null values - Zaniolo - 1984 |

60 | Constraint Programming and Database Query Languages. Invited paper, Symposium on Theoretical Aspects of Computer Software - Kanellakis, Goldin - 1994 |

51 | Problem of Incomplete Information in Relational Databases - Grahne - 1991 |

47 | A Closed Form for Datalog Queries with Integer Order - Revesz - 1990 |

42 | A recursive algebra for nested relations - Colby - 1990 |

38 | Incomplete objects — a data model for design and planning applications - Imieliński, Naqvi, et al. - 1991 |

36 | A semantics for complex objects and approximate answers - Buneman, Davidson, et al. - 1991 |

33 | On databases with incomplete information - Lipski - 1981 |

31 | Variable Independence and Aggregation Closure
- Chomicki, Goldin, et al.
- 1996
(Show Context)
Citation Context ...se the notation VolI(X) for Vol(X \[0� 1] n ) (any other bounding boxcanbechosen without loss of generality). The rst approach to getting a closed language with aggregation proposed in the literature =-=[CGK96]-=- was based on variable independence. We saythatin a constraint tuplet, variablesxandy are independent if there is no atomic formula intthat mentions bothxandy. These two variables are independent in a... |

31 | Semantic representations and query languages for or-sets - Libkin, Wong - 1996 |

24 | Aspects of Partial Information in Databases - Libkin - 1994 |

23 | A formal approach to null values in database relations - Biskup - 1981 |

20 | On the orthographic dimension of constraint databases
- Grumbach, Rigaux, et al.
(Show Context)
Citation Context ... concept of variable independence turned out to be useful in constraint query optimization. Suppose we are given a constraint relationS R n de ned by aformula'(~x1�:::�xn). The orthographic dimension =-=[GRS99]-=- ofS is the maximum size of a subset of variables~y that is independent from its complement. One phenomenon observed in [GRS99] is that while many algorithms on constraint databases run in time O(N f ... |

19 | A relational algebra for complex objects based on partial information - Libkin - 1991 |

18 | Types for data-oriented languages - Cardelli |

18 | Measuring Infinite Relations - Chomicki, Kuper - 1995 |

13 | Exact and approximate aggregation in constraint query languages
- Benedikt, Libkin
(Show Context)
Citation Context ... that the approach based on variable independence does indeed give us a closed language� however, the restriction seems too drastic for most applications. Perhaps a more promising approach is that of =-=[BL99]-=- which extends FO+Poly with a safe application of standard relational aggregation, and shows that volumes of semi-linear sets are then de nable, without any variable independence restrictions. Also no... |

11 | Can datalog be approximated - Chaudhuri, Kolaitis - 1994 |

10 | Convex Spaces as an Order-theoretic Basis for Problem Solving - Ngair - 1992 |

9 | OR-SML: a functional database programming language for disjunctive information and its applications - Gunter, Libkin - 1994 |

9 | Tutorial: Languages for Collection Types - Tannen - 1994 |

8 | The mixed powerdomain. Theoretical Computer Science 103 - Gunter - 1992 |

7 | Modal Theory: An Algebraic Approach to Order, Geometry and Convexity - Romanowska, Smith - 1985 |

6 |
A sweep-plane algorithm for computing the volume of polyhedra represented
- Bieri, Nef
- 1983
(Show Context)
Citation Context ... sets, and A (~x)s are mutually exclusive� moreover, the original set can be represented as W (A ^B ). If a semi-linear set is of nite measure, then its volume is a rational number (see, for example, =-=[BN83]-=-) and hence de nable over hR� +� ;� 0� 1�<i. Moreover, one can e ectively test if a semi-linear set is of nite measure, by testing for the existence of a bounding box outside of which the set has lowe... |

6 | The snack powerdomain for database semantics - Puhlmann - 1993 |

2 | Finding nonrecursive envelopes for database predicates - Chaudhuri |

1 |
Variable independence in theories with quanti er elimination
- Libkin
- 1999
(Show Context)
Citation Context ...ot only recovered, but can even be stated for a larger class of semi-algebraic sets. The proof is a bit involved and will appear elsewhere� however, I can announce the result here. Proposition 5 (see =-=[Li99]-=-) Given a semi-algebraic set S R n , its orthographic dimension is computable, and for every two variablesxi andxj it is decidable if they are independent. 2 4 Closed languages and variable independen... |