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Algebraic GraphOriented = Category Theory Based  Manifesto of categorizing database theory
, 1996
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The graphbased logic of ERdiagrams and taming heterogeneity of semantic data models
, 1997
"... The first goal of the paper is to explicate the formal logic underlying ERdiagrams, ERDlogic. It is shown that this logic is a logic of predicates over setandfunction diagrams, that is, a graphbased logic. Main principles of graphbased logics are developed, in particular, a principal distinct ..."
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The first goal of the paper is to explicate the formal logic underlying ERdiagrams, ERDlogic. It is shown that this logic is a logic of predicates over setandfunction diagrams, that is, a graphbased logic. Main principles of graphbased logics are developed, in particular, a principal distinction between a logical specification as such and its visual presentation is carefully drawn and demonstrated in a number of examples. The approach is based on a generalization of the sketch logic developed in the mathematical category theory, our version was designed to adapt the idea for conceptual modeling. Following category theory, specifications of the language we propose are also called sketches, and so the ERDlogic is manifested as the sketch logic. The second goal of the paper is to demonstrate that the problem of semantic models heterogeneity can be naturally managed in the sketch framework. It is shown that data specifications in many of conventional semantic models can be consider...
CATEGORICAL DATASPECIFICATIONS
, 1995
"... We introduce MDsketches, which are a particular kind of Finite Sum sketches. Two interesting results about MDsketches are proved. First, we show that, given two MDsketches, it is algorithmically decidable whether their model categories are equivalent. Next we show that dataspecifications, as use ..."
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We introduce MDsketches, which are a particular kind of Finite Sum sketches. Two interesting results about MDsketches are proved. First, we show that, given two MDsketches, it is algorithmically decidable whether their model categories are equivalent. Next we show that dataspecifications, as used in databasedesign and software engineering, can be translated to MDsketches. As a corollary, we obtain that equivalence of dataspecifications is decidable.
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
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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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...