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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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Algebraic GraphOriented = Category Theory Based  Manifesto of categorizing database theory
, 1996
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A Diagrammatic Logic for ObjectOriented Visual Modeling
 Electronic Notes in Theoretical Comp. Sci
, 2008
"... 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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Cited by 15 (8 self)
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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 careful motivation and justification of the applicability of generalized sketches for formalizing practical modeling notations. According to the needs in practical modeling we extend the sketch formalism by dependencies and developed new semantic notions based on the Instancesastypedstructures idea. We show that this new framework fits in the general institutional pattern of logic management [14,17] and is well amenable to algebraic manipulations of categorical metalogic.
Formalizing Graphical Schemas for Conceptual Modeling: SketchBased Logic vs.Heuristic Pictures
 IN 10TH INT.CONGRESS OF LOGIC,METHODOLOGY AND PHILOSOPHY OF SCIENCE
, 1995
"... In the paper a new approach to semantic modeling and view integration is proposed. The underlying data model is graphbased yet completely formalized so that graphical schemas themselves are precise specifications suitable for implementation. The formalism is a kind of graphobjectbased generalizat ..."
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Cited by 10 (9 self)
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In the paper a new approach to semantic modeling and view integration is proposed. The underlying data model is graphbased yet completely formalized so that graphical schemas themselves are precise specifications suitable for implementation. The formalism is a kind of graphobjectbased generalization of the relational data model: analytical assertions about elements (values) are replaced by synthetic assertions about diagrams of sets (object classes) and functions (references); correspondingly, queries are operations on such diagrams. On the other hand, the approach is an adaptation of a familiar in the mathematical category theory specification framework based on the so called sketches. On this ground, a new approach to view integration is suggested. Its distinctive characteristics is in the way of specifying correspondence between different views of the same universe of discourse. The specifications are formalized and based on equations which reduces the integration task to a se...
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 9 (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...
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 approached ..."
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Cited by 1 (0 self)
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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...
Algebraic GraphOriented = CategoryTheoryBased Manifesto of Categorizing DataBase Theory Third version
, 1995
"... Foreword. Category theory is well known as a highlevel polymorphic framework suitable for specifying complex structures and formalisms. Quite unexpectedly, however, it turned out that even elementary category theory notions can be valuable in practice of software engineering (see [18, 9, 12]), and ..."
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Foreword. Category theory is well known as a highlevel polymorphic framework suitable for specifying complex structures and formalisms. Quite unexpectedly, however, it turned out that even elementary category theory notions can be valuable in practice of software engineering (see [18, 9, 12]), and in the summer of 1994 we wrote a manifesto ([7], the first version of the present one) to claim our belief in the extreme fruitfulness of incorporating the category theory (CT) machinery into the database (DB) area. That time we did not know about works by Johnson with coauthors (see [18] for references) which seem to be the first publications on the real influence of CT machinery in the DB field. So, a real mutual liking between CT and DB is about two years old. We cannot say that their relations were unclouded during these years, and now we recognize quite clearly that theoretical achievments do not directly lead to revolutions in the field of information (and any other) technologies: the normal way of changes in the latter is the way of more or less rapid evolution only more or less modulated by theoretical ideas. Nevertheless, we consider the last year as a confirmation of our previous predictions: the list of (CT+DB)publications is actually growing (though not so rapidly as we hoped), and at a recent International Workshop ([6]) there was a special section on (CT+DB), and methodologies