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Algebraic GraphBased Approach to Management of MultiBase Systems,II: Mathematical Aspects of Schema Integration
 TR9502, FRAME INFORM SYSTEMS
, 1995
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Databases as Diagram Algebras: Specifying Queries and Views Via the GraphBased Logic of Sketches
, 1996
"... The goal of the paper is to develop a graphical formalism for specifying queries and views within the sketch data model (SkeDM) introduced in [17]. Sketches are directed multigraphs in which some diagrams are labeled with special markers. These markers denote predicates and operations over diagrams ..."
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Cited by 9 (7 self)
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The goal of the paper is to develop a graphical formalism for specifying queries and views within the sketch data model (SkeDM) introduced in [17]. Sketches are directed multigraphs in which some diagrams are labeled with special markers. These markers denote predicates and operations over diagrams of sets and functions. Given a signature of operations (query language), any sketch (database schema) can be extended with derived items denoting data that can be retrieved from the database. Views to a schema S are then sketch morphisms v : SV ! S 0 from some sketch (view schema) SV into an augmentation of S with derived items, S 0 . In this way one obtains a unifying graphbased formal language for data and metadata definition and manipulation. In particular, a formalized specification framework for heterogeneous multibase systems can be built. The approach is described with a number of examples and then precisely formalized. The main technical contribution is the development of alge...
Databases as Graphical Algebras: Algebraic GraphBased Approach to Data Modeling and Database Design
, 1996
"... . The approach we suggest is based on a graphical specification language possessing formal semantics so that graphical images themselves are precise specifications suitable for implementation. Our specifications are similar to the sketches developed in the category theory but, in contrast to them, ..."
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Cited by 8 (5 self)
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. The approach we suggest is based on a graphical specification language possessing formal semantics so that graphical images themselves are precise specifications suitable for implementation. Our specifications are similar to the sketches developed in the category theory but, in contrast to them, enjoy the possibility of setting arbitrary signatures of diagram properties and operations. An important (and sometimes crucial) step in the process of database design is schema (or view) integration, that is, an activity aimed at producing a global conceptual schema of a database from a set of locally developed useroriented schemas (views). In our approach, correspondence between semantic schemas to be integrated is specified by equations so that the integration procedure can be reduced to algebraic manipulations with sketches representing schemas. This provides the possibility of automated view integration and, correspondingly, automated database design. In the paper the mathemat...
A Graphical Yet Formalized Framework for Specifying View Systems
, 1997
"... A graphical formalized language is proposed for specifying systems of views over database schemas. The language is based on the notion of arrow (mapping) between data schemas and is suitable for any data model for which schema mappings are defined. In particular, the constructs of query, query langu ..."
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Cited by 7 (6 self)
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A graphical formalized language is proposed for specifying systems of views over database schemas. The language is based on the notion of arrow (mapping) between data schemas and is suitable for any data model for which schema mappings are defined. In particular, the constructs of query, query language, view and view integration can be consistently expressed in this arrow formalism and correspondingly specified. This gives rise to a general graphbased framework for specifying complex view systems. Basic constructions of the language and the entire framework as well can be considered as specialization of very general constructs developed in the mathematical category theory. 1 Introduction The notion of view is one of the central ones in the database (DB) technology. Views make it possible to provide each application with its own presentation of data and isolate them from inessential (for them) details and changes of DB schemas. The practical importance of views is commonly recognized...
Formalizing Schemas for Federal Database Environment Architecture
, 1997
"... . The aim of the paper is to suggest a formalized datamodelindependent language for metadata modeling. That is, the paper explains notions of database schema, instance, query language and view in some abstract way without using specifics of one or another data model. This gives rise to a universal ..."
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Cited by 2 (2 self)
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. The aim of the paper is to suggest a formalized datamodelindependent language for metadata modeling. That is, the paper explains notions of database schema, instance, query language and view in some abstract way without using specifics of one or another data model. This gives rise to a universal metadata model suitable for specifying heterogeneous federated database systems. In particular, a formalized schema of heterogeneous federal database environment is built. The framework is based on ideas of graphical logic and algebra developed in the mathematical category theory. The latter can be considered as a precise discipline of arrow (graphical) thinking. So, in a wider context, the paper is an attempt to incorporate arrow thinking into the theoretical foundations of CoopIS and set them on the firm mathematical ground. ? Supported by Grants 93.315 and 96.0316 from the Latvian Council of Science ?? Supported partially by Grant 314/9472II (the scheme for research collaboration wit...
The Arrow Logic of Metadata Environment: A Formalised GraphBased Framework for Structuring Metadata Repositories
, 1997
"... . A graphical formalized language is proposed for structuring metadata environments. The language is based on the notion of mapping (morphism) between data schemas and suitable for any data model for which schema morphisms are defined. In particular, the constructs of view, refinement and schema int ..."
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Cited by 1 (1 self)
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. A graphical formalized language is proposed for structuring metadata environments. The language is based on the notion of mapping (morphism) between data schemas and suitable for any data model for which schema morphisms are defined. In particular, the constructs of view, refinement and schema integration can be expressed in our arrow formalism and correspondingly specified. On this ground a general graphbased pattern is proposed for structuring data schema libraries. Basic constructions of the language and the entire framework as well can be considered as specializations of very general constructs developed in the mathematical category theory. This provides the language with a firm mathematical foundation. A distinctive feature of the framework is its algebraic nature. In particular, it is shown that the well known problems of view updateability and lossless refinement can be algebraically formulated in a mutually dual way. ? Supported by Grants 93.315 and 96.0316 from the Latvian...
Generalised Sketches as an algebraic graphbased framework for semantic modeling and database design
, 1997
"... . A graphbased specification language and the corresponding machinery are described as stating a basic framework for semantic modeling and database design. It is shown that a few challenging theoretical questions in the area, and some of hot practical problems as well, can be successfully approache ..."
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. A graphbased specification language and the corresponding machinery are described as stating a basic framework for semantic modeling and database design. It is shown that a few challenging theoretical questions in the area, and some of hot practical problems as well, can be successfully approached in the framework. The machinery has its origin in the classical sketches invented by Ehresmann and is close to their generalization recently proposed by Makkai. There are two essential distinctions from Makkai's sketches. One consists in a different  more direct  formalization of sketches that categorists (and database designers) usually draw. The second distinction is more fundamental and consists in introducing operational sketches specifying complex diagram operations over ordinary (predicate) sketches, correspondingly, models of operational sketches are diagram algebras. Together with the notion of parsing operational sketches, this is the main mathematical contribution of the pape...
Some Suggestions on Mathematics Relevant to the Database Theory
"... . In the paper there is discussed a mathematical framework suitable for specificational problems of modern theory of databases. The main thesis is that a proper framework for a majority of hot problems should be built on the ground of graphbased logic and algebra as opposed to stringbased logics a ..."
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. In the paper there is discussed a mathematical framework suitable for specificational problems of modern theory of databases. The main thesis is that a proper framework for a majority of hot problems should be built on the ground of graphbased logic and algebra as opposed to stringbased logics and algebras over sets currently employed in the DB theory. Such a graphbased machinery was developed in the mathematical category theory so that the latter can provide a proper foundation. The general problem of building the categorial framework for the DB theory is decomposed into a sequence of special tasks. ? Supported by Grant 94.315 from the Latvian Council of Science Since the seminal Codd's papers, databases (DBs) became one of the most theoretically supported branches of computer technologies. Indeed, the seventies were the time of relational model (RDM), and a major factor in that success was the existence of data definition/manipulation languages possessing precise yet easyto...