## Semantic Representations And Query Languages For Or-Sets (1993)

### Cached

### Download Links

- [ftp.cis.upenn.edu]
- [ftp.cis.upenn.edu]
- [sdmc.krdl.org.sg:8080]
- [ftp.cis.upenn.edu]
- [ftp.cis.upenn.edu]
- DBLP

### Other Repositories/Bibliography

Venue: | IN PROCEEDINGS OF 12TH ACM SYMPOSIUM ON PRINCIPLES OF DATABASE SYSTEMS |

Citations: | 32 - 18 self |

### BibTeX

@INPROCEEDINGS{Libkin93semanticrepresentations,

author = {Leonid Libkin and Limsoon Wong},

title = {Semantic Representations And Query Languages For Or-Sets},

booktitle = {IN PROCEEDINGS OF 12TH ACM SYMPOSIUM ON PRINCIPLES OF DATABASE SYSTEMS},

year = {1993},

pages = {37--48},

publisher = {}

}

### OpenURL

### Abstract

Or-sets were introduced by Imielinski, Naqvi and Vadaparty for dealing with limited forms of disjunctive information in database queries. Independently, Rounds used a similar notion for representing disjunctive and conjunctive information in the context of situation theory. In this paper we formulate a query language with adequate expressive power for or-sets. Using the notion of normalization of or-sets, queries at the "structural" and "conceptual" levels are distinguished. Losslessness of normalization is established for a large class of queries. We have obtained upper bounds for the cost of normalization. An approach related to that of Rounds is used to provide semantics for or-sets. We also treat or-sets in the context of partial information in databases.

### Citations

11403 |
Computers and Intractability: A Guide to the Theory of NP-Completeness
- Garey, Johnson
- 1979
(Show Context)
Citation Context ...ystem of distinct representatives of elements of x (which aresor-sets) whose size is atsmost k. The problem of finding a system of distinct representatives of sizes5 k is known tosbe NP-complete, see =-=[9]-=-. Therefore, the problem whether Q(k, x) evaluates tostrue issNP-complete.s7 Future WorksThere are many further problems which we would like to investigate. The languages we have proposedsgive rise to... |

778 | Rewrite systems
- Dershowitz, Jouannaud
- 1990
(Show Context)
Citation Context ...ject of type t there exists its unique representation at the conceptual level whose type is the normalsform of t.sTo state these results precisely, we need some definitions about rewrite systems, see =-=[8]-=-. If a signaturesis fixed, a rewrite system is a set of rules of form rl - 72 where TI, r 2sare terms. If a is obtainedsfrom r by rewriting a subterm of r, we also write T - a. If a is obtained from r... |

762 | Notions of computation and monads - Moggi - 1991 |

466 | Comprehending monads
- WADLER
- 1992
(Show Context)
Citation Context ...anguage.)sThe algebraic version of the language is used in this report. We denote this language by NRsZ(C)swhere C are some additional primitives like operations on integers. As observed by Wadler in =-=[25]-=-,sthe same syntax can be used for many "collection" types besides sets. In particular, by replacing thesset operators of NR4 by the corresponding operators for or-sets, a language for programming with... |

350 |
Incomplete information in relational databases
- ImielinĚski, Lipski
- 1984
(Show Context)
Citation Context ...he S~nyth powerdomain does notscontain the empty set. Observe that if X is totally unordered, sb is the subset and _<fl is the supersetsordering on non-empty sets. The Hoare ordering was also used in =-=[14]-=- to order relations with partialsinformation. We will try to justify using sb to order values of the set types and <f to order the valuessof the or-set types.sAssume that a set AsC X is given. How can... |

150 | A Logical Language for Data and Knowledge Bases - Naqvi, Tsur - 1989 |

132 | Principles of programming with complex objects and collection types. Theor - Buneman, Naqvi, et al. - 1995 |

131 | Naturally embedded query languages
- BREAZU-TANNEN, BUNEMAN, et al.
- 1992
(Show Context)
Citation Context ...rtys[16] which contains some hyperexponential queries.s2 Structural Query LanguagesA nested relational language based on the idea of structural recursion [4, 31 and on monads [20,s251 was proposed in =-=[5]-=-. This language is of polynomial time complexity and smoothly generalizessmany approaches to nested relational algebras, cf. [2]. It is extensible and has an appealing syntax.sFor example, (x I x E no... |

123 | On the Power of Languages for the Manipulation of Complex Objects - Abiteboul, Beeri - 1988 |

117 |
On cliques in graphs
- Moon, Moser
- 1965
(Show Context)
Citation Context ...sets). Then itsfollowssfrom the definition of a that Yl, . . . , Yp are precisely the cliques of G. Since n = size x = w, applyingsthe upper bound on the number of cliques for a graph with n vertices =-=[21]-=-, we obtain p = m(x) 5 fln.sCase 4. x = (XI, .s. . ,Xk)swhere Xi's are or-sets of a base type. Then normalize(x) = or-p(x) andsm(x) 5 n. Again, simple arithmetic shows that n < $6". Hence, m(x) 5 an.s... |

108 | Structural recursion as a query language - BREAZU-TANNEN, BUNEMAN, et al. - 1991 |

67 | Logical and computational aspects of programming with sets/bags/lists - Breazu-Tannen, Subrahmanyam - 1991 |

65 | Using powerdomains to generalize relational databases
- Buneman, Jung, et al.
(Show Context)
Citation Context ...known, nonexistent, existent unknown - is another example of ordering on objects.sIn fact, a general approach to the treatment of partial information as ordering on the set of objectsswas proposed in =-=[7]-=- and further developed in [6, 181. We remark here that this approach is also suitablesfor databases without partial information. In such a case, values of base types are totally unordered.sAssume that... |

47 |
The Definition of Standard ML
- Harper, Milner, et al.
- 1991
(Show Context)
Citation Context ... -+ bool for each object type s ,sand a collectionsof constants c of base type Type(c). Type superscripts are usually omitted because the most generalstype of any given morphisms can be inferred (see =-=[12]-=- for example).sSemantics. nl and n2 are first and second projections. ! maps anything to the unique element ofstype unit. (f ,g) is pair formation, f o g is the composition of f and g. id is the ident... |

39 | Some properties of query languages for bags - Libkin, Wong - 1994 |

38 |
Incomplete objects - data model for design and planning applications
- Imielinski, Naqvi, et al.
- 1991
(Show Context)
Citation Context ... of or-sets are complementary. Consider a design template used by an engineer. Thestemplate may indicate that component A can be built by either module B or module C. Such astemplate, as explained in =-=[15]-=-, is structurally a complex object whose component A is the or-sets*An extended abstract of this paper will appear in The Proceedings of the 12th Symposium on Principles of DatabasesSystems, 1993.s'Su... |

36 |
A semantics for complex objects and approximate answers
- Buneman, Davidson, et al.
(Show Context)
Citation Context ...moved in some situations. But we do not yet have a full characterization of thosessituations.sThere are various sophisticated order theoretic models of partial information in databases - sand-swiches =-=[6]-=-, mixes [lo], snacks [17, 231. They enjoy universality properties and therefore can be in-scorporated into the programming language syntax. We plan to investigate the applicability of suchsmodels to t... |

26 | Sensory Communication - Jung - 1961 |

23 | Aspects of Partial Information in Databases - Libkin - 1910 |

23 | Conservativity of nested relational calculi with internal generic functions - Libkin, Wong - 1994 |

20 |
The mixed power domain
- Gunter
- 1992
(Show Context)
Citation Context ...me situations. But we do not yet have a full characterization of thosessituations.sThere are various sophisticated order theoretic models of partial information in databases - sand-swiches [6], mixes =-=[lo]-=-, snacks [17, 231. They enjoy universality properties and therefore can be in-scorporated into the programming language syntax. We plan to investigate the applicability of suchsmodels to the study of ... |

20 |
Powerdomains and modality
- Winskel
- 1983
(Show Context)
Citation Context ...a(U). By claim 2, g(B) <tisAj for some Aj. Hence, ming(B) <tisAj and since A is ansantichain w.r.t. I#, A; = Aj = ming(B) E Pa(f?). This finishes the proof of claim 3 and the theorem.sIt was shown in =-=[26]-=- that the orderings sb and <n can be given a logical interpretation. Motivated bysapplications in the semantics of concurrent programming, Winskel used the modal connectives ands0 to describe sb and I... |

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

14 | Normalizing incomplete databases - Libkin - 1995 |

12 | Complexity tailored design: a new design methodology for databases with incomplete information - IMIELINSKI, MEYDEN, et al. - 1995 |

11 |
Situation-theoretic aspects of databases
- Rounds
- 1991
(Show Context)
Citation Context ...anguage cansexpress queries of hyper-exponential complexity. Nevertheless, they were successful in identifyingscertain restricted tractable fragments that are useful in real-life applications.sRounds =-=[24]-=- studied complex object databases from the situation-theoretic point of view. Connectionsswith natural language problems motivated him to introduce the notions of conjunctive and disjunctivesinformati... |

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

9 |
Querying Design and Planning Databases
- Imielinski, Naqvi, et al.
- 1991
(Show Context)
Citation Context ... on assigningsobject identifiers, and demonstrated a sufficient condition for order-independence. In addition, theyswere able to demonstrate a coNP-complexity result for tha.t particular proposal. In =-=[16]-=- they studiedssome intrinsic lower bounds on complexity of LVC-style [22] queries on or-sets. The language cansexpress queries of hyper-exponential complexity. Nevertheless, they were successful in id... |

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

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

7 | An elementary proof that upper and lower powerdomain constructions commute
- Libkin
(Show Context)
Citation Context ...to be {a;(l), . . . , a Y(~)). Thensa,(A) = min b(max f (A))sf G 3 . 4s5sFurthermore, the famous result that iterated powerdomains a,re isomorphic [13] can now be given asvery simple description (cf. =-=[19]-=-):sTheorem 1 a, establishes an isomorphism between [{(t))], and [({t))],. The converse Pa issPa(A) = m us< Is(minfs(A)), A E [({t))Ila- f E 3 ds-sProof. We have to show that a,smaps [{(t))] to [({t))]... |

7 | On powerdomains and modality. Theoretical Computer Science, 36:127--137 - Winskel - 1985 |

6 | Hoare and Smyth power domain constructors commute under composition - Flannery, Martin - 1990 |

6 | Lower and upper power domain constructions commute on all cpos
- Heckmann
(Show Context)
Citation Context ...chsthat 1 < f (i) 5 ni. For f E FA, f (A) is defined to be {a;(l), . . . , a Y(~)). Thensa,(A) = min b(max f (A))sf G 3 . 4s5sFurthermore, the famous result that iterated powerdomains a,re isomorphic =-=[13]-=- can now be given asvery simple description (cf. [19]):sTheorem 1 a, establishes an isomorphism between [{(t))], and [({t))],. The converse Pa issPa(A) = m us< Is(minfs(A)), A E [({t))Ila- f E 3 ds-sP... |

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

4 | Rewrite systems, in "Handbook of Theoretical Computer Science - Dershowitz, Jouannaud - 1990 |

3 | Approximation in databases, in "LNCS 893 - Libkin - 1995 |

2 | The mixed powerdomain, Theoret - Gunter - 1992 |

2 | Algebraic characterization of edible powerdomains - Libkin - 1993 |

2 | A Logical Language for Data and Knowledge Bases", Computer - Naqvi, Tsur - 1989 |

2 | Semantic Domains, in "Handbook of Theoretical Computer Science - Gunter, Scott - 1990 |

2 | Querying design and planning databases, in "LNCS 566 - Imielinski, Naqvi, et al. - 1991 |

1 | Situation-theoretic aspects of databases, in "CSLI 26 - Rounds |

1 |
A Logical Language for Data and Ii'nowledge Bases", Computer
- Naqvi, Tsur
- 1989
(Show Context)
Citation Context ... for order-independence. In addition, theyswere able to demonstrate a coNP-complexity result for tha.t particular proposal. In [16] they studiedssome intrinsic lower bounds on complexity of LVC-style =-=[22]-=- queries on or-sets. The language cansexpress queries of hyper-exponential complexity. Nevertheless, they were successful in identifyingscertain restricted tractable fragments that are useful in real-... |