P. Buneman, S. Davidson, A. Watters, A semantics for complex objects and approximate answers, Journal of Computer and System Sciences 43 (1991), 170--218.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....In other words, we need a set of operations to manipulate such semistructured data. In the past decade, the similar problem, that is, manipulating data with partial and or incomplete information, has been investigated in depth in the context of relational, complex object and multiple databases [5, 7, 13, 16 18, 22, 23, 27, 30]. Speci c operations such as union, intersection [5] and join [7] are introduced to manipulate such data. However, these works focus on typed data and support only homogeneous sets and tuples. Thus, it is dicult to directly apply them on semistructured data, where although the data may have some ....

.... decade, the similar problem, that is, manipulating data with partial and or incomplete information, has been investigated in depth in the context of relational, complex object and multiple databases [5, 7, 13, 16 18, 22, 23, 27, 30] Speci c operations such as union, intersection [5] and join [7] are introduced to manipulate such data. However, these works focus on typed data and support only homogeneous sets and tuples. Thus, it is dicult to directly apply them on semistructured data, where although the data may have some structure, the structure is not as rigid, regular, or complete as ....

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O. P. Buneman, S. B. Davidson, and A. Watters. A Semantics for Complex Objects and Approximate Answers. J. Computer and System Sciences, 43(1):170-218, 1991. Mengchi Liu and Tok Wang Ling

....to the state of its predecessor. A set of paths may be determined by a path expression. For example, the path expression Store. Address determines the set of paths (1, 2) 8, 9) since 1 is identifier of an object labeled by Store, 2 is identifier of an object labeled by Address, and 2 val(1) [2, 3]. The path expression Store.Address closes the set (1, 2) 8, 9) The closure consists of all paths with prefixes belonging to the closed set. Thus, the value of the expression Store. Address is the set (1, 2) 8, 9) 8, 9, 11) 8, 9, 12) Store, Store. Address and Store.Address are ....

....well as between object identifiers. Now, we can formalize the notion of subsumption by means of partial ordering relations. We will use three partial ordering relations, which have been used in the study of the semantics of programs [13] feature structures [4] and value oriented complex objects [2, 3, 9]. The orderings under considerations are: partial ordering for disjunctive sets, s (Smyth X Y y c Y. 3 x c X. x y; partial ordering for conjunctive sets, Hoare s X Y x cX. 3y Y.x y; partial ordering for convex sets, Plotkin s X y X y X s Y. Note, that ....

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Buneman O. P., Davidson S.B., Waters A., A semantics for complex objects and approximate answers, Journal of Computer and System Sciences, No. 43, pp. 170-218, 1991.

....formulated against databases of labeled objects, we define partial pre ordering relation on these objects. We will use three well known partial ordering relations, which have been used in the study of the semantics of programs [ 18] feature structures [6] and value oriented complex objects [3,5,13,16]. The orderings are: partial ordering for disjunctive sets, s (Smyth ordering) partial ordering for conjunctive sets, Hoare s ordering) and partial ordering for convex sets, Plotkin s ordering) which combines the two previous, i.e. X Y : X Y X y. Note, that ....

Buneman O. P., Davidson S.B., Waters A., A semantics for complex objects and approximate answers, Journal of Computer and System Sciences, No. 43, pp. 170-218, 1991.

....For instance, references [25,26] study the approximate fixpoints of Datalog predicates, and [27] uses approximate predicates as filters for expensive ones. Second, several researchers have explored accelerated but approximated query answering [28 31] to reduce response time. Third, reference [32] develops a framework for representing approximate complex objects and supporting queries over them. Finally, CoBase [33] explored query relaxation for approximate answering. We define our translation metrics based on the precision and recall parameters. Both classic notions have been commonly ....

P. Buneman, S. B. Davidson, and A. Watters. A semantics for complex objects and approximate answers. Journal of Computer and System Sciences, 43(1):170--218, Aug. 1991.

....can conclude with certainty that they belong to the answer to Q. The upper approximation to the answer to Q consists of those objects for which one can conclude that they may belong to the answer to Q. However, it was not until ten years later that it was observed by Buneman, Davidson and Watters [5] that those pairs of approximations may not only be regarded as results of query evaluation, but may also be used as a representation mechanism for certain kinds partial data. Moreover, this kind of partiality is different from traditional models such as null values and disjunctive information. If ....

....is a TA; therefore, CS1 gives us the certain part of the answer. Moreover, every TA is an employee, hence finding people in Employees who are not represented in CS1 gives us the possible part of the answer to the TA query. A pair of relations CS1 and Employees is called a sandwich (for TA) cf. [5]. The Employees relation is an upper bound: every TA is an Employee. The CS1 relation is a lower bound: every entry in CS1 represents a TA. We are looking for the set of TA something that s in between; hence the name. Notice that the records in CS1 and Employees are consistent: for every record ....

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P. Buneman, S. Davidson, A. Watters, A semantics for complex objects and approximate answers, JCSS 43(1991), 170--218.

....following: given a set of databases D1 ; Dn and a query q that can not be answered by using information from one of D i s, approximate the answer to q by using information from all D1 ; Dn . These problems have been investigated and they gave rise to a number of theoretical models [5, 10, 21, 15]. Given a query q, the databases are divided into two groups, one giving the upper approximation to the answer to q (that corresponds to possible information) and the other giving the lower approximation (that corresponds to the definite information) Here we demonstarte how OR SML can be used to ....

....This also allows us to take joins and meet of records. For example, John 15K John 076 = John 15K 076 and John 15K John 076 = John . Notice that the join of two records is not necessarily defined. The theory of partial information conveyed by means of partial orders was worked out in [5, 6, 12, 14]. For instance, for ordering collections the following two extensions of partial orders have been considered: X [ Y , 8x 2 X 9y 2 Y : x y and X ] Y , 8y 2 Y 9x 2 X : x y. In [17] it was argued that [ is better suited for ordering sets while ] is better suited for ordering or sets. ....

[Article contains additional citation context not shown here]

P. Buneman, S. Davidson, A. Watters, A semantics for complex objects and approximate answers, JCSS 43:170--218, 1991.

....given a set of databases D 1 ; D n and a query q that can not be answered by using information from one of D i s, approximate the answer to q by using information from all D 1 ; D n . These problems have been investigated and they gave rise to a number of theoretical models [5, 11, 22, 16]. Intuitively, given a query q, the 13 databases are divided into two groups, one giving the upper approximation to the answer to q (that corresponds to possible information) and the other giving the lower approximation (that corresponds to the definite information) It has been shown in [11, 16] ....

....This also allows us to take joins and meet of records. For example, John 15K John 076 = John 15K 076 John 15K John 076 = John Notice that the join of two records is not necessarily defined. The theory of partial information conveyed by means of partial orders was worked out in [5, 6, 13, 15]. For instance, for ordering collections the following two extensions of partial orders have been considered: X [ Y , 8x 2 X 9y 2 Y : x y and X ] Y , 8y 2 Y 9x 2 X : x y 14 In [18] it was argued that [ is better suited for ordering sets while ] is better suited for ordering ....

[Article contains additional citation context not shown here]

P. Buneman, S. Davidson, A. Watters, A semantics for complex objects and approximate answers, Journal of Computer and System Sciences 43(1991), 170--218.

....programs that are evaluated on databases consistent with fds. Lambrichts et al. 7] also look into the problem of integrating functions in datalog and supply a test for consistency for a class of datalog programs including functions, negation, and a strong type system. Lakshmanan and Hern andez [6] give a procedure to factor out goals from a class of linear sirups under the presence of fds. Torlone and Atzeni [14] study the problem of updating consistent deductive databases wrt fds. Sadri has found some sufficient conditions for solving the FD FD implication problem in linear datalog ....

....of recursive rule queries. In Proc. Fifth ACM SIGACT SIGMOD Symposium on Principle of Database Systems, pages 280 293, 1986. 5] A. Gonzalez Tuchmann. The chase of datalog programs. PhD thesis, New Mexico State University, Department of Computer Science, Las Cruces, NM 88003 0001, 1995. [6] L. V. S. Lakshmanan and H. J. Hern andez. Structural query optimization a uniform framework for semantic query optimization in deductive databases. In Proc. Tenth ACM SIGACT SIGMOD SIGART Symposium on Principle of Database Systems, pages 102 114, 1991. 7] E. Lambrichts, P. Nees, J. ....

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O. P. Buneman, S. B. Davidson, and A. Watters. A semantics for complex objects and approximate answers. J. Computer and System Sciences, 43(1):170--218, 1991.

....in a database may be incomplete. Hence, both tuples and sets can be partial or complete. 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. Specific operators such as union [3] and join [5] 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 been investigated in Relationlog [8] An operator ....

....similar to the traditional immediate consequence operator, but incorporates typing constraints and may not be complete. Now we introduce the grouping operator G which is used to integrate partial information into complete information. It generalizes the union operator in [3] the join operator in [5], the grouping operator in [8] and incorporates the partition normal form introduced in [9] The grouping operator G is defined recursively on a set of objects as follows: 1. G(fOg) O if O is complete. 2. G(fO 1 ; On ; g) 3. G(fO 1 ; On ; g) G(fO 1 ; On g) 4. If S is a ....

O. P. Buneman, S. B. Davidson, and A. Watters. A Semantics for Complex Objects and Approximate Answers. J. Computer and System Sciences, 43(1):170--218, 1991.

....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 ....

.... 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 structure, the structure is not as rigid, regular, or ....

[Article contains additional citation context not shown here]

O. P. Buneman, S. B. Davidson, and A. Watters. A Semantics for Complex Objects and Approximate Answers. J. Computer and System Sciences, 43(1):170-- 218, 1991.

....In other words, we need a set of operations to manipulate such semistructured data. In the past decade, the similar problem, that is, manipulating data with partial and or incomplete information, has been investigated in depth in the context of relational, complex object and multiple databases [5, 7, 13, 16 18, 22, 23, 27, 30]. Speci c operations such as union, intersection [5] and join [7] are introduced to manipulate such data. However, these works focus on typed data and support only homogeneous sets and tuples. Thus, it is dicult to directly apply them on semistructured data, where although the data may have some ....

.... past decade, the similar problem, that is, manipulating data with partial and or incomplete information, has been investigated in depth in the context of relational, complex object and multiple databases [5, 7, 13, 16 18, 22, 23, 27, 30] Speci c operations such as union, intersection [5] and join [7] are introduced to manipulate such data. However, these works focus on typed data and support only homogeneous sets and tuples. Thus, it is dicult to directly apply them on semistructured data, where although the data may have some structure, the structure is not as rigid, regular, or complete as ....

[Article contains additional citation context not shown here]

O. P. Buneman, S. B. Davidson, and A. Watters. A Semantics for Complex Objects and Approximate Answers. J. Computer and System Sciences, 43(1):170-218, 1991.

....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 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 ....

P. Buneman, S. Davidson, and A. Watters. A semantics for complex objects and approximate answers. Journal of Computer and System Sciences, 43(1):170--218, August 1991.

....instance, references [26, 27] study the approximate fixpoints of Datalog predicates, and [28] uses approximate predicates as filters for expensive ones. Second, several researchers have explored accelerated but approximated query answering to reduce response time [29, 30, 31, 32] Third, reference [33] develops a framework for representing approximate complex objects and supporting queries over them. Finally, CoBase [34] explored query relaxation for approxi M Q Q M false positive false negative Figure 1: Venn diagram of a query Q and its mapping M . mate answering. We define our ....

P. Buneman, S. B. Davidson, and A. Watters. A semantics for complex objects and approximate answers. Journal of Computer and System Sciences, 43(1):170--218, Aug. 1991.

....and meets of records. For example, John 15K John 076 = John 15K 076 and John 15K John 076 = John . Notice that the join of two records is not necessarily defined. In our solution we rely on the theory of partial information conveyed by means of partial orders which was worked out in [3, 4, 9, 10]. In particular, we use the fact that orders can be defined at arbitrary types, and consequently we have an OR SML library of orderings and functions meet; join : s Theta s hsi (the empty or set indicates a non existent join or meet; otherwise a singleton or set is produced) Using these ....

.... = let fun compattoX (X,x) Set.ormember(mkboolco(true) orsmap (fn z = compat(z,x) X) in Set.select (fn z = compattoX (R,z) S end; val newcs1 = removeanomaly compatible (emp,cs1) val newcs1 = John , 76) Sally , 120) co Now consider the solution proposed in [3] (see also [6] Given an element x 2 CS1, let y 1 ; yn be those elements in Employees that can be joined with x. Then x 0 = V i (x y i ) is called a promotion of x. Intuitively, it adds all information about x from Employees. The solution to the TA query is to take all promotions ....

P. Buneman, S. Davidson, A. Watters, A semantics for complex objects and approximate answers, JCSS 43:170--218, 1991.

....which one can conclude with certainty that they belong to the answer to Q. The upper approximation to Q consists of those objects for which one can conclude that they may belong to the answer to Q. However, it was not until ten years later that it was observed by Buneman, Davidson and Watters [5] that those pairs of approximations may not only be regarded as the results of 1 query evaluation, but may also be used as a representation mechanism for certain kinds of partial data. Moreover, this kind of partiality is different from traditional models such as null values and disjunctive ....

....in CS1 is a TA, CS1 gives us the certain part of the answer. Moreover, every TA is an employee, hence finding people in Employees who are not represented in CS1 gives us the possible part of the answer to the TA query. The pair of relations CS1 and Employees is called a sandwich (for TA) cf. [5]. The Employees relation is an upper bound: every TA is an Employee. The CS1 relation is a lower bound: every entry in CS1 represents a TA. We are looking for the set TA something that s in between; hence the name. Notice that the records in CS1 and Employees are consistent: for every record ....

[Article contains additional citation context not shown here]

P. Buneman, S. Davidson, A. Watters, A semantics for complex objects and approximate answers, Journal of Computer and System Sciences 43(1991), 170--218. 39

....is not reduced. By requiring all objects to be reduced, we obtain a partial order on objects which is referred to as the Hoare ordering in the literature. However, such a notion is too restrictive as it disallows meaningful objects like ffenglishg; fenglish; frenchgg to exist in the database. In [15] and [35] the notion of cochain is used. Two objects o 1 and o 2 are considered equivalent if o 1 o 2 and o 2 o 1 . Let [o] denote an equivalence class. The sub object relationship is then extended to equivalence classes by [o 1 ] o 2 ] iff o 1 o 2 . The set of equivalence classes is called ....

O. P. Buneman, S. B. Davidson, and A. Watters. A semantics for complex objects and approximate answers. J. Computer and System Sciences, 43(1):170--218 (1991).

....M Q Q M false positive false negative Figure 1: Venn diagram of a query Q and its mapping M . approximate predicates as filters for expensive ones. Second, several researchers have explored accelerated but approximated query answering to reduce response time [29, 30, 31, 32] Third, reference [33] develops a framework for representing approximate complex objects and supporting queries over them. Finally, CoBase [34] explored query relaxation for approximate answering. We define our translation metrics based on the parameters of precision and recall. Both classic notions have been commonly ....

P. Buneman, S. B. Davidson, and A. Watters. A semantics for complex objects and approximate answers. Journal of Computer and System Sciences, 43(1):170--218, Aug. 1991.

.... (besides the mentioned Dyreson s bibliography) major database journals and conference proceedings in the field covering last several years, and made an extensive search in the bibliographic WWW database (http: www.informatik.uni trier.de ley db index.html) In the result we have discovered items [BDW90, GYPB92, INV91, Lenz91, Motr90, TYI89, VrLi91, VrLi93, Zica90], presenting continuations or generalizations of the ideas known from the relational school. They make no comment concerning how they intend to avoid very low practical impact that plagued their relational predecessors. Null values and unions are not mentioned in the object oriented manifesto ....

P. Buneman, S.B. Davidson, A. Watters. A Semantics for Complex Objects and Approximate Answers. Journal of Computer and System Sciences, Aug.1990, pp.170-218.

....area. In the database community, it was felt that the logic programming paradigm offers interesting opportunities as a database query language. This resulted in logical query languages like LDL [14] and NAIL [13] So called complex objects have recently been studied for use in database systems [7, 8]. Much of what has been proposed in those studies is derived from earlier work extending first order terms to terms [1] The latter notion has had a more direct application in programming language design [4, 2, 6] than in database systems. Still, the functionality and naturalness of deductive ....

....and experimentation, we use the specific language LIFE [2] but this implies no loss of generality. Indeed, although we formulate it using terms, our design is directly applicable to any logical query language with complex objects represented as Prolog terms or as data structures a la [7, 8], since all these models turn out to be special cases of terms. We present the theoretical view of our proposed database support of that language and discuss the results. Our theoretical design was put into practice as the basis of an experimental implementation [12] Although our experiment may ....

O. Peter Buneman, Susan D. Davidson, and Aaron Watters. A semantics for complex objects and approximate answers. Journal of Computer and System Sciences, 43(1):170--218 (August 1991).

....all others put together. Rejecting a nice idea of Peter Buneman to call it the kitchen sink powerdomain, I shall use the salad powerdomain instead. Let me first motivate the use of the edible powerdomains. Since late 70s, many researchers tried to understand partial information in databases; [1, 14, 9, 23, 6, 5, 17] name just a few of the many books and papers in this area. In [5, 6] Buneman and others proposed to recast the main principles of relational databases in domain theory. The ordering on objects was interpreted as partiality, i.e. x y means that x is more partial than y, or y is more informative ....

....sink powerdomain, I shall use the salad powerdomain instead. Let me first motivate the use of the edible powerdomains. Since late 70s, many researchers tried to understand partial information in databases; 1, 14, 9, 23, 6, 5, 17] name just a few of the many books and papers in this area. In [5, 6] Buneman and others proposed to recast the main principles of relational databases in domain theory. The ordering on objects was interpreted as partiality, i.e. x y means that x is more partial than y, or y is more informative than x. For example, Name Joe , Age ] Name Joe , Age ....

[Article contains additional citation context not shown here]

P. Buneman, S. Davidson, A. Watters, A semantics for complex objects and approximate answers, Journal of Computer and System Sciences 43(1991), 170--218.

....for which one can conclude with certainty that they belong to the answer to the query. The upper approximation consists of those objects for which one can conclude that they may belong to the answer. However, it was not until ten years later that it was observed by Buneman, Davidson and Watters [3] that those pairs of approximations may not only be regarded as results of query evaluation, but may also be used as a representation mechanism for certain kinds partial data. Moreover, this kind of partiality is different from traditional models such as null values and disjunctive information. If ....

....Employees who are not represented in CS1 gives us the possible part of the answer to the TA query. Employees: Name Salary Room John 15K Ann 17K Mary 12K Michael 14K CS1: Name Salary Room John 076 Michael 320 A pair of relations CS1 and Employees is called a sandwich (for TA) cf. [3]. The Employees relation is an upper bound: every TA is an employee. The CS1 relation is a lower bound: every entry in CS1 represents a TA. We are looking for the set of TA something that s in between; hence the name. Notice that the records in CS1 and Employees are consistent: for every record ....

[Article contains additional citation context not shown here]

P. Buneman, S. Davidson, A. Watters. A semantics for complex objects and approximate answers. JCSS 43(1991), 170--218.

....complex attribute values. The attribute values can be changed but such changes have no effect on the object s identity. Classes can have subclasses and attributes defined on superclasses are inherited by subclasses. Subclasses of a class must be declared explicitly. In complex object data models [7, 9, 22], objects are represented by structured values such as nested tuples and sets. There isn t a notion of object identity. Instances and subclasses of classes are inferred rather than asserted. On the other hand, deductive query languages such as Datalog [10] extend the expressive power of ....

O. P. Buneman, S. B. Davidson, and A. Watters. A semantics for complex objects and approximate answers. J. Computer and System Sciences, 43:170--218, 1991.

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P. Buneman, S. Davidson, A. Watters, A semantics for complex objects and approximate answers, Journal of Computer and System Sciences 43 (1991), 170--218.

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Peter Buneman, Susan B. Davidson, and Aaron Watters. A semantics for complex objects and approximate answers. Journal of Computer and System Sciences, 43(1):170-218, August 1991. 187

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P. Buneman, S. Davidson, A. Watters, A semantics for complex objects and approximate answers, JCSS 43(1991), 170--218.

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