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A Probabilistic Relational Algebra for the Integration of Information Retrieval and Database Systems
 ACM Transactions on Information Systems
, 1994
"... We present a probabilistic relational algebra (PRA) which is a generalization of standard relational algebra. Here tuples are assigned probabilistic weights giving the probability that a tuple belongs to a relation. Based on intensional semantics, the tuple weights of the result of a PRA expression ..."
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Cited by 206 (34 self)
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We present a probabilistic relational algebra (PRA) which is a generalization of standard relational algebra. Here tuples are assigned probabilistic weights giving the probability that a tuple belongs to a relation. Based on intensional semantics, the tuple weights of the result of a PRA expression always confirm to the underlying probabilistic model. We also show for which expressions extensional semantics yields the same results. Furthermore, we discuss complexity issues and indicate possibilities for optimization. With regard to databases, the approach allows for representing imprecise attribute values, whereas for information retrieval, probabilistic document indexing and probabilistic search term weighting can be modelled. As an important extension, we introduce the concept of vague predicates which yields a probabilistic weight instead of a Boolean value, thus allowing for queries with vague selection conditions. So PRA implements uncertainty and vagueness in combination with the...
A Paraconsistent Relational Data Model
 International Journal of Computer Mathematics
, 1995
"... We present a generalisation of the relational data model based on a 4valued paraconsistent logic. Our data model is capable of manipulating incomplete as well as inconsistent information. For this model, we define algebraic operators that are generalisations of the usual operators, such as union, s ..."
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Cited by 16 (8 self)
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We present a generalisation of the relational data model based on a 4valued paraconsistent logic. Our data model is capable of manipulating incomplete as well as inconsistent information. For this model, we define algebraic operators that are generalisations of the usual operators, such as union, selection, join, on ordinary relations. Our data model can underlie any database management system that deals with incomplete or inconsistent information. As another application of our model and its algebra, we present a bottomup method for constructing the weak wellfounded model of general deductive databases. This method can be very simply extended to construct the wellfounded model.
Semantics for Null Extended Nested Relations
 ACM TODS
, 1993
"... this paper we define the semantics of nested relations, which may contain null values, in terms of integrity constraints, called null extended data dependencies, which extend functional dependencies and join dependencies encountered in flat relational database theory. We formalise incomplete informa ..."
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Cited by 16 (1 self)
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this paper we define the semantics of nested relations, which may contain null values, in terms of integrity constraints, called null extended data dependencies, which extend functional dependencies and join dependencies encountered in flat relational database theory. We formalise incomplete information in nested relations by allowing only one unmarked generic null value,
An extension of the relational data model to incorporate ordered domains
 ACM Transactions on Database Systems
, 2001
"... We extend the relational data model to incorporate partial orderings into data domains, which we call the ordered relational model. Within the extended model, we define the Partially Ordered Relational Algebra (the PORA) by allowing the ordering predicate ⊑ to be used in formulae of the selection op ..."
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Cited by 11 (2 self)
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We extend the relational data model to incorporate partial orderings into data domains, which we call the ordered relational model. Within the extended model, we define the Partially Ordered Relational Algebra (the PORA) by allowing the ordering predicate ⊑ to be used in formulae of the selection operator (σ). The PORA expresses exactly the set of all possible relations which are invariant under orderpreserving automorphism of databases. This result characterises the expressiveness of the PORA and justifies the development of Ordered SQL (OSQL) as a query language for ordered databases. OSQL provides users with the capability of capturing the semantics of ordered data in many advanced applications, such as those having temporal or incomplete information. Ordered Functional Dependencies (OFDs) on ordered databases are studied, based on two possible extensions of domain orderings: (1) pointwiseordering and (2) lexicographical ordering. We present a sound and complete axiom system for OFDs in the first case and establish a set of sound and complete chase rules for OFDs in the second. Our results suggest that the implication problems for both cases of OFDs are decidable and that the enforcement of OFDs in ordered relations are practically feasible. In a wider perspective, the proposed model explores an important area of objectrelational databases, since ordered domains can be viewed as a general kind of data type. Categories and Subject Descriptors: H.2.1 [Database Management]: Logical Design—data
On Codd Families of Keys over Incomplete Relations
, 2010
"... Keys allow a database management system to uniquely identify tuples in a database. Consequently, the class of keys is of great significance for almost all data processing tasks. In the relational model of data, keys have received considerable interest and are well understood. However, for efficient ..."
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Cited by 9 (7 self)
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Keys allow a database management system to uniquely identify tuples in a database. Consequently, the class of keys is of great significance for almost all data processing tasks. In the relational model of data, keys have received considerable interest and are well understood. However, for efficient means of data processing most commercial relational database systems deviate from the relational model. For example, tuples may contain only partial information in the sense that they contain socalled null values to represent incomplete information. Codd’s principle of entity integrity says that every tuple of every relation must not contain a null value on any attribute of the primary key. Therefore, a key over partial relations enforces both uniqueness and totality of tuples on the attributes of the key. On the basis of these two requirements, we study the resulting class of keys over relations that permit occurrences of Zaniolo’s null value ‘noinformation’. We show that the interaction of this class of keys is different from the interaction of the class of keys over total relations. We establish a finite ground axiomatization, and an algorithm for deciding the associated implication problem in linear time. Further, we characterize Armstrong relations for an arbitrarily given sets of keys; that is, we give a sufficient and necessary condition for a partial relation to satisfy a key precisely when it is implied by a given set of keys. We also establish an algorithm that computes an Armstrong relation
Accessing geographical metafiles through a database storage system
 In Advances in Spatial Databases. Fourth International Symposium SSD'95, edited by M. Egenhofer
, 1995
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Searching a minimal semanticallyequivalent subset of a set of partial values
"... Imprecise data exist in databases due to their unavailability or data/schema incompatibilities in a multidatabase system. The notion of partial values has been employed for representing imprecise data. Manipulation of partial values is therefore needed for processing queries involving imprecise data ..."
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Cited by 2 (2 self)
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Imprecise data exist in databases due to their unavailability or data/schema incompatibilities in a multidatabase system. The notion of partial values has been employed for representing imprecise data. Manipulation of partial values is therefore needed for processing queries involving imprecise data. In this paper, we study the problem of eliminating redundant partial values which may result from a projection on an attribute with partial values. The redundancy of partial values is defined through the interpretation of a set of partial values. This problem is equivalent to searching a minimal semanticallyequivalent subset of a set of partial values. A semanticallyequivalent subset contains exactly the same information as the original set. We derive a set of useful properties and apply a graph matching technique to develop an efficient algorithm for searching such a minimal subset and therefore eliminating redundant partial values. By this process, we not only provide a concise answer to the user, but also reduce the communication cost when partial values are requested to be transmitted from one site to another site in a distributed environment. Moreover, further manipulation of the partial values can be simplified. Finally,
The database now includes 18 healthy subjects (13 females and 5 males, with ages between 20 and 50, average 34.3 years), and 12 congestive heart failure subjects (3 females and 9 males, with ages between 22 and 71, average 60.8 year) in sinus rhythm
 Journal of Database Management
, 2001
"... Data warehousing is a corporate strategy that needs to integrate information from several sources of separately developed Database Management Systems (DBMSs). A future DBMS of a data warehouse should provide adequate facilities to manage a wide range of information arising from such integration. We ..."
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Cited by 1 (1 self)
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Data warehousing is a corporate strategy that needs to integrate information from several sources of separately developed Database Management Systems (DBMSs). A future DBMS of a data warehouse should provide adequate facilities to manage a wide range of information arising from such integration. We propose that the capabilities of database languages should be enhanced to manipulate userdefined data orderings, since business queries in an enterprise usually involve order. We extend the relational model to incorporate partial orderings into data domains and describe the ordered relational model. We have already defined and implemented a minimal extension of SQL, called OSQL, which allows querying over ordered relational databases. One of the important facilities provided by OSQL is that it allows users to capture the underlying semantics of the ordering of the data for a given application. Herein we demonstrate that OSQL aided with a package discipline can be an effective means to manage the interrelated operations and the underlying data domains of a wide range of advanced applications that are vital in data warehousing, such as temporal, incomplete and fuzzy information. We present the details of the generic operations arising from these applications in the form of three OSQL packages called: OSQL_TIME, OSQL_INCOMP and OSQL_FUZZY. Data warehousing is a corporate strategy that addresses a broad range of decision support requirements such as
Strong keys and functional dependencies . . .
, 2010
"... We study keys and functional dependencies in the context of partial relations that permit null values with the interpretation no information. Based on Codd’s principle of entity integrity we propose the class of strong keys over partial database relations. These keys enforce both uniqueness and tot ..."
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We study keys and functional dependencies in the context of partial relations that permit null values with the interpretation no information. Based on Codd’s principle of entity integrity we propose the class of strong keys over partial database relations. These keys enforce both uniqueness and totality of tuples. We study the interaction of strong keys with Lien, Atzeni and Morfuni’s classes of functional dependencies and nullfree subschemata. For various subclasses we establish axiomatisations, lineartime algorithms to decide implication, and characterisations and computations of Armstrong relations. Interestingly, the class of general functional dependencies does not enjoy Armstrong relations over partial relations, but even the combined class of strong keys and standard functional dependencies does. We also settle various questions related to the maximal size of a family of nonredundant strong keys over partial relations.