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Algebraic GraphOriented = Category Theory Based  Manifesto of categorizing database theory
, 1996
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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 3 (3 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.
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 integ ..."
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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.
Comparison of Categorical Foundations of ObjectOriented Database Model
 In: Proceedings of 5th International Conference on Deductive and ObjectOriented Databases, Montreaux, CH
, 1997
"... . The present development in the database area is highly influenced by the objectoriented principles of data modeling. On the contrary to the previously successful relational approach, it lacks rigorous theoretical support. This problem is mainly due to the fact that the semantics description of su ..."
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Cited by 1 (0 self)
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. The present development in the database area is highly influenced by the objectoriented principles of data modeling. On the contrary to the previously successful relational approach, it lacks rigorous theoretical support. This problem is mainly due to the fact that the semantics description of such features as generalization, specialization, encapsulation, and inheritance is not trivial by using just the means of the set theory. Therefore, many researchers focused on finding suitable theoretical means for the modeling of complex objects. This paper is concerned with the comparison of categorical modeling in the database area and proposes a limit data model that enables to represent the objects, relationships, multiple inheritance, class polymorphism and virtual methods in the categorical setting. The aim to formalize these notions arose from the actual need. We would like to use it to support the development of an objectoriented database model closely following the standard ODMG'93...
Methods in The ObjectOriented Model as Sums of Morphisms
, 1997
"... The present development in the database area is highly influenced by the objectoriented principles of data modelling. But on the contrary to the previously successful relational approach it lacks rigorous theoretical support. This problem is mainly due to the fact that semantics description of such ..."
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The present development in the database area is highly influenced by the objectoriented principles of data modelling. But on the contrary to the previously successful relational approach it lacks rigorous theoretical support. This problem is mainly due to the fact that semantics description of such features as generalization, specialization, encapsulation and inheritance is not trivial using just the means of the set theory. This paper presents one way of formal specification of methods in objectoriented database model. The mathematical means of sum of morphisms in category theory proved to be useful for this purpose.
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...
Extending an ObjectOriented Model: Multiple Class Objects
, 1997
"... . Experiences of both researchers and practitioners with the development of objectoriented database systems help us to evaluate the real contributions of objectoriented modeling principles and show the limits and possibilities of improvements of the objectoriented model. One of the research areas ..."
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. Experiences of both researchers and practitioners with the development of objectoriented database systems help us to evaluate the real contributions of objectoriented modeling principles and show the limits and possibilities of improvements of the objectoriented model. One of the research areas where such a need was recognized concerns the class membership. In most objectoriented data model objects must belong to a single most specific class. However, the real world situations often break this presumption. The aim of this paper is to discuss the issues relating to an extension of modeling concepts to capture the objects that can belong to the multiple most specific classes. Our final objective is to present a framework for the formal objectoriented models that will provide the rigorous theoretical tool to solve issues concerning conflicts that can arise in structural components of objects. Most importantly, we show that the structural conflicts can be solved from the context det...
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