L. Libkin, Approximation in databases, in "LNCS 893: Proceedings of 5th International Conference on Database Theory," Springer Verlag, January 1995.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....component called Snarks [17] The reasoning component is based on a method that is both complete for finite satisfiability and complete for unsatisfiability. This method is based on the ideas in [6, 7, 4, 20] 2 and is a refinement of the method underlying the model generator Satchmo [21, 9], which was originally developed for this kind of applications [4] The visualisation component was originally developed as a debugging tool for Satchmo and variants thereof. Its interactive features can provide support for investigating interesting database states in the case of finite ....

....in the style of SIC. 3 A Method Complete for Unsatisfiability and for Finite Satisfiability The reasoning component of SIC is based on the Extended Positive Tableaux method (short EP Tableaux method) 8] This method extends the PUHR Tableaux method [9] underlying 28 the model generator Satchmo [21]. A major feature of the PUHR Tableaux method is that it generates only positive facts, leaving negative information implicit, which is a most natural approach for database applications. On the other hand, the PUHR Tableaux method is not complete for finite satisfiability, i.e. even if a set of ....

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L. Libkin. Approximation in databases. In Proceedings of the International Conference on Data Base Theory, pages 414--424, Prague, Czech Republic, 1995. Springer-Verlag LNCS 326. 154

....spread in several sources to obtain a comprehensive description of the object. In the past several years, a sub problem, that is, integrating data with partial and complete tuples and or partial sets, has been investigated in depth in the context of relational and complex object databases [5, 7, 11, 14, 20, 21, 22, 28, 29, 30, 31, 39, 40]. Specific operators such as union [5] and join [7] are introduced to integrate partial information. However, these works focus on typed data and support homogeneous sets and tuples. Thus, it is difficult to apply them directly on semistructured data, where although the data may have some ....

....data which have been represented in our framework. We propose a new operator integration for this purpose and discuss its semantic properties. 1. 1 Related Work There has been a lot of work on the integration of heterogeneous data sources, such as multiple databases or data sources on the web [5, 7, 14, 20, 21, 22, 23, 28, 29, 30, 31, 37, 39, 40, 10]. In particular, there are two questions closely related to our study. One is how to decide that two objects mentioned in two different sources refer to the same entity in the world. Another is how to reconcile partial or inconsistent data values from sources referring to the same entity. Most ....

L. Libkin. Approximation in Databases. In Proceedings of the International Conference on Data Base Theory, pages 414--424, Prague, Czech Republic, 1995. Springer-Verlag LNCS 326.

....database. Both systems propose an approach based on approximate query processing. In presence of unavailable data, the system returns an approximate answer which is defined in terms of subsets and supersets sandwiching the exact answer. Approximation has been notably developed in [5] 6] [15]. Multiplex uses the notions of subview and superview to define the approximate answer. A view V1 is a subview of a view V2 if it is obtained as a combination of selections and projections of V2; V2 is then a superview of V1. These notions can be a basis to define the relationship between a query ....

L. Libkin. Approximation in databases. In Proceedings of the International Conference on Database Theory, 1995.

....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, Approximation in databases, in "LNCS 893: Proceedings of 5th International Conference on Database Theory," 411--424, Prague, Czech Republic, January 1995.

....that the concept of a finite anti chain, which took the role of a relation in [4] has to be replaced by a more refined construction. Conceptually convincing and mathematically satisfying appears to be the idea of a snack, invented by Buneman and studied in [17,19] Related structures appear in [7,15]. Snacks can be explained quite easily: If we take the point of view that a relation is basically a set structured in a certain way then once partial information comes into the picture, the natural choice is to work with approximations to sets. This approximation can be achieved in two different ....

L. Libkin. Approximation in databases. In G. Gottlob and M. Vardi, editors, International Conference on Database Theory, volume 893 of Lecture Notes in Computer Science, pages 411--424. Springer Verlag, 1995.

....of sure and of maybe tuples. It seems that except from negation S null P Gamma coincides with the computation of sure tuples and S null P coincides with that of maybe tuples in Biskup s approach. Buneman et al. 4] study a generalization of partial tuples for complex objects and Libkin [10] gives a general account of approximations in databases. As mentioned in the introduction, we regard the enhancement of logic programs with more sophisticated representation mechanisms as highly important. The combination of ideas presented in this paper with complex objects seems to be promising. ....

Leonid Libkin. Approximation in databases. In Georg Gottlob and Moshe Y. Vardi, editors, Proc. of the 5th Int. Conf. on Database Theory, pages 411--424. Springer, Lecture Notes in Computer Science 893, 1995.

....is how to obtain information as complete as possible from such a database. In other words, what is the intended semantics of such a database. In the past several years, a sub problem, that is, a database which contains partial and complete tuples and or partial sets, has been investigated in depth [4, 6, 9, 13, 14, 15, 19, 20, 21, 22, 27]. Specific operators such as union [4] and join [6] are introduced to integrate partial information. However, complete sets are not supported and all sets are treated simply as partial sets. Another sub problem, that is, a database which contains partial and complete sets and complete tuples, has ....

L. Libkin. Approximation in Databases. In Proceedings of the International Conference on Data Base Theory, pages 414--424, Prague, Czech Republic, 1995. Springer-Verlag LNCS 326.

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L. Libkin, Approximation in databases, in "LNCS 893: Proceedings of 5th International Conference on Database Theory," Springer Verlag, January 1995.

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L. Libkin. Approximation in databases. In G. Gottlob and M. Vardi, eds., LNCS 893: Proc. Internat. Conference on Database Theory, Prague,

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L. Libkin, Approximation in databases, in "LNCS 893: Proceedings of 5th International Conference on Database Theory, Prague, January 1995," 411--424.

....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 are others; see, for example, BDW91, Lib95a] There are no solid theoretical foundations for any of these, nor are there any results that show how they are connected. Moreover, most models of partiality are developed only for the flat relational model, and virtually nothing is known for more complicated database models. This situation in ....

L. Libkin. Approximation in databases. In G. Gottlob and M. Vardi, editors, LNCS 893: Proceedings of International Conference on Database Theory, Prague, 1995, pages 411--424. Springer-Verlag, 1995.

.... 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 called multisets) as the underlying model. While there was a flurry of activity in studying many aspects of bag based databases query language design, expressive power and complexity, ....

....0 . X OWA 7 Gamma Y iff X CWA 7 Gamma Y or X Y . Let v CWA and v OWA denote the transitive reflexive closure of CWA 7 Gamma and OWA 7 Gamma . That is, X v CWA Y or X v OWA Y if Y is obtained from X by a sequence of allowed updates that add information. Proposition 2. 1 (See [9, 8]. X v OWA Y iff X H Y , and X v CWA Y iff X P Y . Moreover, this continues to hold when subsets are restricted to antichains and updates are modified in such a way that after each update only maximal (most informative) elements are retained. 2 We should remark that the Smyth ordering ....

L. Libkin. Approximation in databases. In G. Gottlob and M. Vardi, eds., LNCS 893: Proc. Internat. Conference on Database Theory, Prague, 1995, pages 411--424. Springer-Verlag, 1995.

....of [AH95] saying that tc can be evaluated in A B using polynomial space under a special evaluation strategy. Here we used our space efficient strategy for normalization to achieve the same result. 5 Objects with partial information and antichain semantics The antichain semantics, defined in [Lib95, LW93a] and based on the ideas from [BJO91, Lib91] is used for objects with partial information. The key idea is that the notion of partiality can be conveyed by orderings, with x y meaning that y is more informative than x. This ordering is usually given for base types. For example, a null value ni ....

L. Libkin. Approximation in databases. In LNCS 893: Proc. ICDT-95, pages 411--424.

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L. Libkin. Approximation in databases, In Proc. of Intl. Conf. on Database Theory, pages 411--424, LNCS 893, Springer Verlag, 1995. 40

....operations compute with them. This idea was further developed in Tannen et al. 8] and Buneman et al. 9] where it was suggested that one use operations naturally associated with data types as introduction and elimination operations. The formal category theoretic treatment was given in Libkin [32]. The operations on collections correspond to the categorical notion of a monad [40] We illustrate the use of this approach in the design of the nested relational language NRL. This language deals with complex objects in the form of nested relations. The types of complex objects are given by the ....

....shown recently [20] that equational theories of bag languages with monus are rather complicated. Nevertheless, we believe some useful optimizations can still be found. Finally, we would like to use the results of this report as a basis for extending the approach of Buneman et al. 10] and Libkin [31, 32] to study bags with partial information and to program with them. Initial results in this direction are reported in [38] List of the langauages Language Definition in NRL and its components: NRA;NRC and RSA Section 2 NRL(eq) Section 2 NBL and its components: NBA;NBC and RBA Subsection 3.1 ....

L. Libkin, Approximation in databases, in "LNCS 893: Proceedings of 5th International Conference on Database Theory," Springer Verlag, January 1995.

....size of the normal form. In [16] a logical language was used. We would like to see if the idea can be worked out for our languages. There are various sophisticated order theoretic models of partial information in databases sandwiches [6] mixes [10] snacks [31, 30] and their generalizations [31, 22]. They are used when a real world situation can be approximated from below and above by information in a database. These structures enjoy universality properties and therefore can be incorporated into the programming language syntax [22] We have recently shown [22] that the intimate connection ....

....mixes [10] snacks [31, 30] and their generalizations [31, 22] They are used when a real world situation can be approximated from below and above by information in a database. These structures enjoy universality properties and therefore can be incorporated into the programming language syntax [22]. We have recently shown [22] that the intimate connection between or sets and the Smyth powerdomain can help us use or sets for a suitable representation of those approximation models in the context of database programming languages like or NRA. We plan to further investigate the applicability ....

[Article contains additional citation context not shown here]

L. Libkin, Approximation in databases, in "LNCS 893: Proceedings of 5th International Conference on Database Theory, Prague, January 1995," 411--424.

.... be very useful for analyzing incompleteness of information in the relational database model and its extensions [3, 5, 8, 11] 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, 6, 7]. All of these papers deal with set based databases. However, real database systems frequently use multisets (also called bags) as the underlying model. While there was a flurry of activity in studying many aspects of bag based databases query language design, expressive power and complexity, ....

..... X OWA 7 Gamma Y iff X CWA 7 Gamma Y or X Y . Let v CWA and v OWA denote the transitive reflexive closure of CWA 7 Gamma and OWA 7 Gamma . That is, X v CWA Y or X v OWA Y if Y is obtained from X by a sequence of allowed updates that add information. Proposition 2. 1 (See [8, 7]. X v OWA Y iff X H Y , and X v CWA Y iff X P Y . Moreover, this continues to hold when subsets are restricted to antichains, and updates are modified in such a way that after each update only maximal (most informative) elements are retained. 2 We should remark that the Smyth ordering ....

L. Libkin. Approximation in databases. In G. Gottlob and M. Vardi, eds., LNCS 893: Proc. Internat. Conference on Database Theory, Prague, 1995, pages 411--424. Springer-Verlag, 1995.

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