## A Semantics for Complex Objects and Approximate Queries (1988)

Venue: | In Seventh Symposium on the Principles of Database Systems |

Citations: | 26 - 0 self |

### BibTeX

@INPROCEEDINGS{Buneman88asemantics,

author = {Peter Buneman and Susan Davidson and Aaron Watters},

title = {A Semantics for Complex Objects and Approximate Queries},

booktitle = {In Seventh Symposium on the Principles of Database Systems},

year = {1988},

pages = {305--314}

}

### Years of Citing Articles

### OpenURL

### Abstract

A new definition of complex objects is introduced which provides a denotation for incomplete tuples as well as partially described sets. Set values are "sandwiched" between "complete" and "consistent" descriptions (representing the Smyth and Hoare powerdomains respectively), allowing the maximal values to be arbitrary subsets of maximal elements in the domain of the set. We also examine the use of rules in defining queries over such objects. 1 Introduction A characteristic of "complex-object" [1, 2] databases and "higher-order" relations [3, 4] is that the components of tuples are not restricted to taking only atomic values, but may be other tuples or even sets of tuples. A second property of complex objects and related information structures is that there is a natural ordering on the domain of values with an associated algebra [5, 6, 7]. For example, in Bancilhon and Khoshafian's ordering on tuples [1] [Name) 0 J.Doe 0 ] v [Name) 0 J.Doe 0 ;Age)21] This research was suppor...

### Citations

488 |
Denotational Semantics: The Scott-Strachey Approach to Programming Language Theory
- Stoy
- 1977
(Show Context)
Citation Context ... like the spaces we are using to be rich enough to describe recursive record structures. For this purpose, the appropriate definition of a domain is an !-algebraic consistently complete partial order =-=[11]-=-, and most of the results we will give apply to such domains. However, since all our examples will be of finite, non-recursive structures, the only important property of a domain is that it is a parti... |

349 |
Incomplete information in relational databases
- Imielinski, Lipski
- 1984
(Show Context)
Citation Context ...l elements of D. Unfortunately, if one wants to assign a reasonable semantics to sets of values neither of these orderings in isolation is satisfactory since their maximal elements are uninteresting. =-=[10]-=-, in formalizing incomplete information, describes the semantics of a tuple such as [Name) 0 J.Doe 0 ;Age) ] as f[Name) 0 J.Doe 0 ;Age)i] j i 2 I g where I is the set of all possible (total) values fo... |

271 |
Domains for denotational semantics
- Scott
- 1982
(Show Context)
Citation Context ... be other tuples or even sets of tuples. A second property of complex objects and related information structures is that there is a natural ordering on the domain of values with an associated algebra =-=[5, 6, 7]-=-. For example, in Bancilhon and Khoshafian's ordering on tuples [1] [Name) 0 J.Doe 0 ] v [Name) 0 J.Doe 0 ;Age)21] This research was supported in part by NSF IRI86-10617, NSF MCS 8219196-CER, ARO DAA6... |

179 | Ifo: A formal semantic database model - Abiteboul, Hull - 1987 |

82 |
Power domains
- Smyth
- 1978
(Show Context)
Citation Context ... B j 8b 2 B:9a 2 A:a v b; Both of these orderings are well-known in the study of the semantics of concurrency and non-determinism; v ] and v [ are respectively called the Smyth and Hoare powerdomains =-=[9]-=-. To make v [ and v ] orderings as opposed to a pre-ordering, A and B must be restricted to be co-chains. S is a co-chain in a domain D if any pair of elements in S is incomparable, i.e. if x; y 2 S a... |

80 |
A Calculus for Complex Objects
- Bancilhon, Khoshafian
- 1989
(Show Context)
Citation Context ...alues to be arbitrary subsets of maximal elements in the domain of the set. We also examine the use of rules in defining queries over such objects. 1 Introduction A characteristic of "complex-obj=-=ect" [1, 2] databases-=- and "higher-order" relations [3, 4] is that the components of tuples are not restricted to taking only atomic values, but may be other tuples or even sets of tuples. A second property of co... |

67 |
A complete logical calculus for record structures representing linguistic information
- Rounds, Kasper
- 1986
(Show Context)
Citation Context ... be other tuples or even sets of tuples. A second property of complex objects and related information structures is that there is a natural ordering on the domain of values with an associated algebra =-=[5, 6, 7]-=-. For example, in Bancilhon and Khoshafian's ordering on tuples [1] [Name) 0 J.Doe 0 ] v [Name) 0 J.Doe 0 ;Age)21] This research was supported in part by NSF IRI86-10617, NSF MCS 8219196-CER, ARO DAA6... |

65 | Using powerdomains to generalize relational databases
- Buneman, Jung, et al.
(Show Context)
Citation Context ...nd this ordering is inductively extended to order "complex objects" which are hierarchical structures containing both tuples and sets. In contrast, in an attempt to find a data type for natu=-=ral join, [8]-=- uses the ordering A v ] B j 8b 2 B:9a 2 A:a v b; Both of these orderings are well-known in the study of the semantics of concurrency and non-determinism; v ] and v [ are respectively called the Smyth... |

57 |
An algebraic semantics approach to the effective resolution of type equations
- Aı̈t-Kaci
- 1986
(Show Context)
Citation Context ...ves)L] j [persons)P ] ` O and fY g w ] P and [children)C] ` Y and L = minfX j fXg w ] Cgg] It may be possible to define recursive types and self referencing complex objects using such a notation (see =-=[13]-=-). Another important type of rule we have not yet shown is one where a variable occurs twice on the right hand side. For example we may want to insist that a possible grandparent-child relationship mu... |

54 | A new normal form for nested relations
- Özsoyoglu, Yuan
- 1987
(Show Context)
Citation Context ...nts in the domain of the set. We also examine the use of rules in defining queries over such objects. 1 Introduction A characteristic of "complex-object" [1, 2] databases and "higher-or=-=der" relations [3, 4]-=- is that the components of tuples are not restricted to taking only atomic values, but may be other tuples or even sets of tuples. A second property of complex objects and related information structur... |

36 |
A Lattice Theoretic Approach to Computation Based on a Calculus of Partially Ordered Types
- Ait-Kaci
- 1984
(Show Context)
Citation Context ... be other tuples or even sets of tuples. A second property of complex objects and related information structures is that there is a natural ordering on the domain of values with an associated algebra =-=[5, 6, 7]-=-. For example, in Bancilhon and Khoshafian's ordering on tuples [1] [Name) 0 J.Doe 0 ] v [Name) 0 J.Doe 0 ;Age)21] This research was supported in part by NSF IRI86-10617, NSF MCS 8219196-CER, ARO DAA6... |

20 |
Powerdomains and modality
- Winskel
- 1983
(Show Context)
Citation Context ...e will not discuss here the use of negation to derive complete information from consistent information, or vice versa. For another discussion of the connection between powerdomains and modalities see =-=[12]-=-. In the following we use a slightly abused notation for convenience and readability, writing A w ] O and B v [ O for an sandwich O = (A 0 ; B 0 ) and sets of objects A and B, meaning respectively (A;... |

15 |
Extended algebra and calculus for -1nf relational databases
- Roth, Korth, et al.
- 1984
(Show Context)
Citation Context ...nts in the domain of the set. We also examine the use of rules in defining queries over such objects. 1 Introduction A characteristic of "complex-object" [1, 2] databases and "higher-or=-=der" relations [3, 4]-=- is that the components of tuples are not restricted to taking only atomic values, but may be other tuples or even sets of tuples. A second property of complex objects and related information structur... |