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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...
Model synchronization: mappings, tile algebra, and categories
 In: Postproc. GTTSE
, 2009
"... Abstract. The paper presents a novel algebraic framework for specification and design of model synchronization tools. The basic premise is that synchronization procedures, and hence algebraic operations modeling them, are diagrammatic: they take a configuration (diagram) of models and mappings as th ..."
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Cited by 3 (3 self)
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Abstract. The paper presents a novel algebraic framework for specification and design of model synchronization tools. The basic premise is that synchronization procedures, and hence algebraic operations modeling them, are diagrammatic: they take a configuration (diagram) of models and mappings as their input and produce a diagram as the output. Many important synchronization scenarios are based on diagram operations of square shape. Composition of such operations amounts to their tiling, and complex synchronizers can thus be assembled by tiling together simple synchronization blocks. This gives rise to a visually suggestive yet precise notation for specifying synchronization procedures and reasoning about them. 1
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...
The Next Hundred Diagrammatic Specification Techniques  An Introduction to Generalized Sketches
, 2007
"... ..."
Generalized Sketches: A Universal Logic for Diagrammatic . . .
, 2007
"... Generalized sketches is a graphbased specification format that borrows its main ideas from both categorical and firstorder logic, and adapts them to software engineering needs. In the engineering jargon, it is a modeling language design pattern that combines mathematical rigor and appealing graphi ..."
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Generalized sketches is a graphbased specification format that borrows its main ideas from both categorical and firstorder logic, and adapts them to software engineering needs. In the engineering jargon, it is a modeling language design pattern that combines mathematical rigor and appealing graphical appearance. The paper presents a revised framework of basic concepts to make similarities with the traditional FOL specifications transparent.