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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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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 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...
Heterogeneous View Integration via Sketches and Equations
 In: Foundations of Intelligent Systems, Springer LNAI'1079
, 1996
"... . 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 approach is an adaptation of a familiar in the math ..."
Abstract

Cited by 2 (1 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 approach is an adaptation of a familiar in the mathematical category theory specification framework based on the so called sketches. On this ground, a procedure of automated view integration is developed. Its distinctive feature consists in specifying correspondence between different views (on the same universe of discourse) by equations that reduces the integration task to a sequence of formal algebraic procedures. 1 Introduction and preliminary discussion The term view (or, sometimes, schema) integration refers to the activity aimed at producing a global conceptual schema of an information domain from a set of locally developed useroriented schemas (views). Integration is called heterogeneous if local views are specified in different da...
The Arrow Manifesto: Towards software engineering based on comprehensible yet rigorous graphical specifications
"... . A novel formalizable specification paradigm is proposed which makes it possible to solve a lot of specification problems in software. The roots of the idea are in mathematical category theory; following its terminology we call our specifications sketches. Among the principal advantages of sketches ..."
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Cited by 1 (0 self)
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. A novel formalizable specification paradigm is proposed which makes it possible to solve a lot of specification problems in software. The roots of the idea are in mathematical category theory; following its terminology we call our specifications sketches. Among the principal advantages of sketches are the following. ffl Nice amalgamation of logical rigor and graphical evidence. Sketches are graphbased images yet they are precise formal specifications as rigor as, say, first order logic theories. ffl Universality, in the precise sense of the word. It can be mathematically proven that any specification whose semantic meaning can be formalized can be also expressed by a sketch. ffl Unifying power. Many of graphical specification languages can be simulated by sketches in the corresponding signature of diagram markers. ffl Semantic capabilities. The sketch language is inherently objectoriented and provides a quite natural way of specifying OO classreference schemas. ffl Easy and f...
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...