L. Libkin, L. Wong, Semantic representations and query languages for or-sets, in "Proceedings of 12th ACM Symposium on Principles of Database Systems," Washington, D. C., May 1993. Full version to appear in JCSS.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....set constructor. We therefore consider the weakest order relation that is consistent with the relational model, and is preserved by the application of complex objects constructors. It coincides with order relations previously considered in conjunction with partial informations [BOJ91] and or sets [LW93]. Containment and Equivalence of Queries with Aggregates Complex objects and aggregates are related in a natural way [OOM87] We show how to derive from our results for complex objects new containment and equivalence results for queries with grouping and aggregation over flat relations. In ....

....8i:9i 0 :x i v x 0 i 0 . 2 As a simple example, we have ffa; bg; fa; c; dg; ff; hgg v ffa; b; c; d; eg; ff; hgg because fa; bg v fa; b; c; d; eg, fa; c; dg v fa; b; c; d; eg and ff; hg v ff; hg. This notion of containment has been used previously in partial informations [BOJ91] and or sets [LW93]. It is a particular case of the lower (Hoare) powerdomain ordering [GS90] and it coincides with the simulation relation between complex objects represented as graphs [BDHS96, BDFS97] It is also the smallest order relation for complex objects which is reflexive (x v x) is a congruence (i.e. x ....

Leonid Libkin and Limsoon Wong. Semantic representations and query languages for orsets. In Proceedings of 12th ACM Symposium on Principles of Database Systems, pages 37--48, Washington, D. C., May 1993. See also UPenn Technical Report MS-CIS-92-88.

....mappings are commonly referred to as relations, although this term is overloaded in our context. 6 This extension mode has also been used to lift partial orders (as opposed to general relations) to sets, in work on querying incomplete information. There it is known as the Plotkin ordering [LW93]. Example 2.3 Firstly, we extend the mapping H d = f(1; a) 1; b) 2; b)g, which is not functional in either direction, to sets, to obtain H fdg = f(f1g; fag) f1g; fbg) f1g; fa; bg) f2g; fbg) f1; 2g; fa; bg) f1; 2g; fbg)g. As a second example, consider the mapping H d = f(e; a) i; ....

Leonid Libkin and Limsoon Wong. Semantic representations and query languages for or-sets. In ACM Symposium on Principles of Database Systems, Washington DC, 1993.

....is zip F ; F which is a kind of transpose operator: zip L ; L turns a list of m lists of length n into a list of n lists of length m in the obvious way. 10 A final example of the use of zips is in the approach to query languages for databases with partial information advocated by Libkin and Wong[9, 8]. They combine a collection type (sets or bags) with a version of sets that has a non standard interpretation (but is otherwise identical) the so called or sets. An or set conceptually represents one of the values in it. For normalisation of expressions containing tuples, ordinary sets bags and ....

L. Libkin and L. Wong. Semantic representations and query languages for or-sets. In PODS-93, pages 155--166, 1993.

....[SP94] shows that transitive closure, which is efficiently expressible using structural recursion, has a necessarily exponential implementation in the algebra with powerset of [AB88] The s.r. monad approach can also be used for other collections: languages for or sets [INV91] were studied in [LW93b] and bag languages in [LW94c] see also [GM93] HKM93, HK94] show how to encode related database languages in the simply typed lambda calculus. A central issue is the optimization of collection type queries, see [Sch86, Osb88, Col89, HN91, LD91, LD92, Sar92] and [BK93, ACM93, CV93, CS93, Feg94, ....

Leonid Libkin and Limsoon Wong. Semantic representations and query languages for orsets. In Proceedings of 12th ACM Symposium on Principles of Database Systems, pages 37--48, Washington, D. C., May 1993. See also UPenn Technical Report MS-CIS-92-88.

No context found.

L. Libkin, L. Wong, Semantic representations and query languages for or-sets, in "Proceedings of 12th ACM Symposium on Principles of Database Systems," Washington, D. C., May 1993. Full version to appear in JCSS.

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L. Libkin and L. Wong. Semantic representations and query languages for or-sets. Proc. of the 12th Symposium on Principles of Database Systems, Washington, DC, May 1993, pages 37--48.

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L. Libkin, L. Wong, Semantic representations and query languages for or-sets, in "Proceedings of 12th ACM Symposium on Principles of Database Systems, Washington, D. C., May 1993," 37--48.

....built around datatypes given by the approximation constructs. A straightforward approach results in langauges that have a number of limitations. In an attempt to overcome those limitations, we explain how all the languages can be embedded into a language for conjunctive and disjunctive sets from [22], and demonstrate its usefulness in querying independent databases. Keywords: Independent databases, approximate answers, universality properties, structural recursion, disjunctive information. 1 Supported in part by NSF Grant IRI 90 04137 and AT T Doctoral Fellowship. 1 Introduction The idea ....

....of approximations obtained in section 4. We discuss problems with using this approach, such as undecidability of certain preconditions that need to be checked to ensure well definedness of programs. As a solution to this problem, we suggest an encoding of approximation constructs with or sets [14, 15, 22, 31] and explain how the language for or sets from [22] is suitable for programming with approximations. In fact, a system based on this language [12] has been used in the problems of querying independent databases. 2 Preliminaries Partial objects and ordered sets Most models of partiality of data ....

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L. Libkin and L. Wong, Semantic representations and query languages for or-sets, Proceedings of the 12th Conference on Principles of Database Systems, Washington, DC, May 1993, pages 37--48.

....the form of disjunctive information. In this paper we describe a functional language, OR SML, for querying databases with incomplete and disjunctive information. To handle disjunctive information, we allow a new type constructor of or sets (hence the name OR SML) Or sets have been studied in [13, 17, 23]. The original motivation for or sets came from applications within design, planning, and scheduling areas. Or sets are in essence disjunctive information, but they are distinguished from the latter by having two distinct interpretations. An or set can either be treated at a structural level or at ....

....to follow the approach of [3] which gives a very clean and simple language that has precisely the expressive power of the nested relational algebra. The relational language introduced in [3] was based on earlier languages for lists [27, 28] and it was later generalized to other collection types [17, 18]. The language obtained from the nested relational algebra by adding appropriate primitives dealing with or sets was called or NRA in [17] One of the problems that should be addressed during the language design is a mechanism for incorporating both structural and conceptual queries into the same ....

[Article contains additional citation context not shown here]

L. Libkin and L. Wong, Semantic representations and query languages for or-sets, Proceedings of the 12th PODS, Washington DC, 1993, pages 37--48.

....the form of disjunctive information. In this paper we describe a functional language, OR SML, for querying databases with incomplete and disjunctive information. To handle disjunctive information, we allow a new type constructor of or sets (hence the name OR SML) Or sets have been studied in [14, 18, 24]. The original motivation for or sets came from applications within design, planning, and scheduling areas. Or sets are in essence disjunctive information, but they are distinguished from the latter by having two distinct interpretations. An or set can either be treated at a structural level or at ....

....follow the approach of [3] which gives a very clean and simple language that has 1 precisely the expressive power of the nested relational algebra. The relational language introduced in [3] was based on earlier languages for lists [28, 29] and it was later generalized to other collection types [18, 19]. The language obtained from the nested relational algebra by adding appropriate primitives dealing with or sets was called or NRA in [18] One of the problems that should be addressed during the language design is a mechanism for incorporating both structural and conceptual queries into the same ....

[Article contains additional citation context not shown here]

L. Libkin and L. Wong, Semantic representations and query languages for or-sets, Proceedings of the 12th Conference on Principles of Database Systems, Washington DC, 1993, pages 37--48.

....it denotes an integer, which is either 24 or 27. That is, there are two different views of or sets: structural, that concerns representation, and conceptual, that concerns meaning. This idea was present in the initial papers on or sets [INV91a, INV91b] and later was formalized and worked out in [LW96] 6 1.4 Toward a general theory There are a number of models for partial information in the database literature. Some of them are quite ad hoc, based on specific needs arising in particular applications. We have seen two sources of partiality: null values and disjunctive information. There ....

....or sets is to look at the semantic domains of iterated types, that is, fhtig and hftgi, and see how they are related. In other words, one has to find out what the relationship between P [ P ] A) and P ] P [ A) is. Here we have the following useful fact. Theorem14. see also [Lib92, LW96] Given a finite set of finite sets X = fX 1 ; Xn g where X i = fx i 1 ; x i k i g, let FX be the set of functions f : f1; ng N such that for any i: 1 f(i) k i . If all X i s are subsets of A, define two maps ff a and fi a as follows: ff a (X ) min f2FX v [ ....

[Article contains additional citation context not shown here]

L. Libkin and L. Wong. Semantic representations and query languages for or-sets. Journal of Computer and System Sciences, 52(1):125--142, 1996.

....information. It is capable of solving a number of problems that typically accompany disjunctive information; in particular, the problems we discussed above. To handle disjunctive information, we allow a new type constructor of or sets (hence the name OR SML) Or sets have been studied in [8, 10, 14]. Or sets are in essence disjunctive information, but they are distinguished from the latter by having two distinct interpretations. The structural level concerns the precise way in which an or set is constructed. The conceptual level sees an or set as representing an object which is equal to some ....

....OR SML supports both views of or sets and therefore can answer conceptual queries. The language design. Our language is based on the functional paradigm. Design of functional database query languages has been studied extensively in the past few years and proved very useful. See, for example [1, 2, 10, 11, 13, 16]. Functional languages have certain advantages over logical languages for complex objects. They have clear syntax, they can be typechecked, their semantics is generally easy to define and they allow a limited form of polymorphism. Since entries in databases are allowed to be or sets possibly ....

[Article contains additional citation context not shown here]

L. Libkin and L. Wong, Semantic representations and query languages for or-sets, Proceedings of the 12th PODS, Washington DC, 1993, pages 37--48.

.... to representing partial information in databases that treats objects as elements of partially ordered sets, where the meaning of the order is being more informative , has proved to be very useful for analyzing incompleteness of information in the relational database model and its extensions [3, 5, 9, 12]. In particular, it has allowed a number of powerful tools from denotational semantics of programming languages to be used to analyze the phenomenon of incomplete information [1, 4, 7, 8] All these papers deal with set based databases. However, real database systems frequently use bags (also ....

....which are sets without comparable elements, they become partial orders. Hoare) X H Y , 8x 2 X 9y 2 Y : x y (Smyth) X S Y , 8y 2 Y 9x 2 X : x y (Plotkin) X P Y , X H Y and X S Y Ordering Sets of Incomplete Objects To define orderings for collections, we adopt the approach of [9]. A collection C 1 is more informative than C 2 if C 2 can be obtained from C 1 by a sequence of elementary updates that add information. This approach reduces the problem of choosing an ordering to the problem of formulating elementary updates. Such updates depend on certain assumptions on ....

[Article contains additional citation context not shown here]

L. Libkin and L. Wong. Semantic representations and query languages for or-sets. Proc. of the 12th Symposium on Principles of Database Systems, Washington, DC, May 1993, pages 37--48.

....information, due to conflicts, partial knowledge and other reasons. Queries against such databases often ask questions about various possibilities encoded by the stored data, rather than the stored data itself. Normalization, which is a mechanism for asking such queries, was presented in [LW93a]; however, it had exponential space complexity. The main goal of this paper is to develop a general theory of answering queries against incomplete databases with disjunctive information, and use it to design practical algorithms for query evaluation. We define the semantics of such databases and ....

....the literature. The idea of using and or trees to develop a new object oriented data model with an ad hoc query facility was exploited in [INV91a, INV91b] The query complexity in this model was analyzed in [IMV89] Recently, a functional query language for databases with disjunctions was designed [LW93a] and implemented [GL94] In these papers two kinds of queries have been distinguished: structural queries ask questions about the data stored in a database, whereas conceptual queries ask questions about the data encoded by the information in a database. To illustrate the difference between the ....

[Article contains additional citation context not shown here]

L. Libkin and L. Wong. Semantic representations and query languages for or-sets. In PODS-93, pages 37--48.

....600 Mountain Avenue, Murray Hill, NJ 07974 USA E mail: libkin bell labs.com Abstract We study the problem of choosing a suitable collection of primitives for querying databases with disjunctive information. Theoretical foundations for querying such databases have been developed in [11, 12]. The main tool for querying disjunctive information has come to be known under the name of normalization. In this paper we show how these theoretical results can lead to practical languages for querying databases with disjunctive information. We discuss a collection of primitives that one may ....

....possible worlds by means of disjunctive information. That is, additional transformation of the data stored in a database is needed in order to answer such queries. The need for distinguishing two classes of queries against databases with disjunctive information is known in the literature, cf. [9, 10, 12, 16]. Queries that ask questions about the representation of possible worlds are called structural, whereas conceptual queries ask questions about the data encoded by the information in a database. For example, consider a template used by a designer (shown in figure 1) It may indicate that part D ....

[Article contains additional citation context not shown here]

L. Libkin and L. Wong. Semantic representations and query languages for or-sets. Journal of Computer and System Sciences, 52(1996), 125--142.

....between structural queries and conceptual queries. At the structural level, an or set is a collection of objects, just as a set is. However, at the conceptual level, an or set represents one element from the or set, while the set continues to represent the whole collection. It was shown in [8, 7] that conceptually equivalent objects can be reduced in a canonical manner to the same object, called its normal form. The normal form is a disjunct of all usual objects (i.e. not involving disjunctive information) represented by the given object prior to normalization. Therefore, one can take the ....

....of OR SML. It also gives a way out of database objects into SML values. This is useful, for example, if you wish to incorporate a query into a tactic or a derived rule of inference. 2 The core language The theoretical language upon which OR SML is based was developed by Libkin and Wong in [8]. In this section we describe this core language, called or NRA, and show how it is built on top of Standard ML. We have changed the names of all constructs of or NRA to the names that are used in OR SML. Types of database objects (also called complex objects in the database literature) are given ....

[Article contains additional citation context not shown here]

L. Libkin and L. Wong, Semantic representations and query languages for or-sets, Proceedings of the 12th Symp. on Principles of Database Systems, Washington DC, 1993, pages 37--48.

....built around datatypes given by the approximation constructs. A straightforward approach results in languages that have a number of limitations. In an attempt to overcome those limitations, we explain how all the languages can be embedded into a language for conjunctive and disjunctive sets from [25], and demonstrate its usefulness in querying independent databases. We also discuss the semantics of approximation constructs and relationship between them. 1 Introduction The idea of using approximate answers to queries against databases with partial information has been known in the database ....

....obtained in section 4 and discuss problems with using this approach. One problem is the undecidability of certain preconditions that need to be checked to ensure well definedness of programs. As a solution to this problem, we suggest an encoding of approximation constructs with or sets [17, 25, 33] and explain how the language for or sets [25] is suitable for programming with approximations. In fact, a system based on this language [15] has been used in the problems of querying independent databases. 2 Preliminaries 2.1 Partial objects and ordered sets Most models of partiality of data ....

[Article contains additional citation context not shown here]

L. Libkin and L. Wong, Semantic representations and query languages for or-sets, Journal of Computer and System Sciences, 52 (1) (1996), 125--142.

....2 (n) Q n i=0 g(i) Let powerset : unique ffi powerbag . It is easy to see that powerset (n) fj0; 1; 2; njg. Therefore, b ffi b map(g) applied to powerset (n) gives us f 1 (n) The proof of the expressibility of f 2 resembles the proof of the expressibility of the ff primitive of [34] for or sets. Again, g is mapped over powerset(n) to obtain fjg(0) g(1) g(n)jg. If at least one of g(i) is 0 (that is, an empty bag) the result is 0. Otherwise each occurrence of ( inside each g(i) is paired with i. The resulting bag is flattened and the powerbag is taken. From this ....

L. Libkin, L. Wong, Semantic representations and query languages for or-sets, in "Proceedings of 12th ACM Symposium on Principles of Database Systems," Washington, D. C., May 1993. Full version to appear in JCSS.

....built around datatypes given by the approximation constructs. A straightforward approach results in langauges that have a number of limitations. In an attempt to overcome those limitations, we explain how all the languages can be embedded into a language for conjunctive and disjunctive sets from [17], and demonstrate its usefulness in querying independent databases. 1 Introduction The idea of using approximate answers to queries against databases with partial information has been known in the database literature for more than ten years. In his classical papers, Lipski [18, 19] suggested to ....

....do not possess universality properties. In section 5 we discuss programming with approximation. We explain problems with using the data oriented approach together with operations arising from the universality properties. Then we we suggest an encoding of approximation constructs with or sets [14, 17] and explain how the language for or sets from [17] is suitable for programming with approximations. 2 Preliminaries Partial objects and ordered sets. Most models of partiality of data can be represented via orderings on values, e.g. 1, 13, 9] In [4, 15, 17] a general approach to the treatment ....

[Article contains additional citation context not shown here]

L. Libkin and L. Wong. Semantic representations and query languages for or-sets. In PODS-93, pages 37--48.

....nested relational language is a natural and elegant generalization of these three proposals. Orderings on bags are necessary to deal with such problems as partial information or effective storage strategies. We study several ways to order bags in section 5. First, the approach of Libkin and Wong [22] is extended to bags and the resulting order is shown to be tractable. Second, we present a way to lift linear orders at base types to linear orders at arbitrary types. It is easily implemented in a simple extension of the ambient language. This linear order is at the heart of proving ....

....databases were considered as subsets of certain partially ordered sets in order to provide rigorous mathematical treatment of partial information, we would like to have an ordering on bags whose intuitive meaning is being more partial . We define such on ordering using techniques proposed in [22] and give its characterization. Even though the ordering appears somewhat awkward, we demonstrate an effective algorithm to test whether two bags are comparable. Secondly, we show that if a linear order is given for all base types, it can be extended to a linear order on the domain of an arbitrary ....

[Article contains additional citation context not shown here]

L. Libkin and L. Wong. Semantic representations and query languages for or-sets. In Proceedings of 12th ACM Symposium on Principles of Database Systems, Washington, D. C., May 1993. To appear. Full paper available as UPenn Technical Report MS-CIS-92-88.

....input, in contrast to the proposal of Imielinski, Naqvi, and Vadaparty [18] which contains some hyperexponential queries. In the last section we briefly describe implementation of the proposed languages and outline some problems for further research. The extended abstract of this paper appeared in [23]. 2 Structural Query Language A nested relational language based on the idea of structural recursion [4, 3] and on monads [25, 30] was proposed in [5] This language is of polynomial time complexity and smoothly generalizes many approaches to nested relational algebras, cf. 2] It is extensible ....

L. Libkin and L. Wong, Semantic representations and query languages for or-sets, In: Proceedings of the 12th Conference on Principles of Database Systems (C. Beeri, ed.), Washington DC, May 1993, pages 37-48.

....input and flat relations as output are expressible in (flat) relational algebra. Because, both flat and nested relational algebra are now seen as natural fragments of a general programming paradigm, we are in a position to extend them to other collection types, though we do not do this here; see [33, 37, 35]. In section 5 we further augment the language with a powerset operation R( cond) to obtain the algebra of Abiteboul and Beeri [1] In view of conservativity over relational algebra, this algebra cannot express functions such as transitive closure and parity test without a potentially expensive ....

....it is shown that nesting at intermediate types does not add expressiveness in presence of aggregate functions and certain generic queries. Other results on expressive power are to be found in [34, 36, 35] Our approach can be used for different collections: languages for or sets were studied in [33, 23, 38] and bag languages in [37] As mentioned before, 54] shows that transitive closure, which is efficiently expressible using structural recursion, has a necessarily exponential implementation in complex object algebra [1] 30] show how to encode related database languages in the simply typed ....

L. Libkin, L. Wong, Semantic representations and query languages for or-sets, in "Proceedings of 12th ACM Symposium on Principles of Database Systems," 37--48, Washington, D. C., May 1993.

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L. Libkin and L. Wong. Semantic representations and query languages for orsets. In Proc. of PODS, 1993.

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L. Libkin and L. Wong. Semantic representations and query languages for orsets. In Proc. of PODS, 1993.

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L. Libkin and L. Wong. Semantic representations and query languages for orsets. In Proc. of PODS, Washington D.C., 1993.

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