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14
Algebraic GraphOriented = Category Theory Based  Manifesto of categorizing database theory
, 1996
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Databases as Diagram Algebras: Specifying Queries and Views Via the GraphBased Logic of Sketches
, 1996
"... The goal of the paper is to develop a graphical formalism for specifying queries and views within the sketch data model (SkeDM) introduced in [17]. Sketches are directed multigraphs in which some diagrams are labeled with special markers. These markers denote predicates and operations over diagrams ..."
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Cited by 9 (7 self)
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The goal of the paper is to develop a graphical formalism for specifying queries and views within the sketch data model (SkeDM) introduced in [17]. Sketches are directed multigraphs in which some diagrams are labeled with special markers. These markers denote predicates and operations over diagrams of sets and functions. Given a signature of operations (query language), any sketch (database schema) can be extended with derived items denoting data that can be retrieved from the database. Views to a schema S are then sketch morphisms v : SV ! S 0 from some sketch (view schema) SV into an augmentation of S with derived items, S 0 . In this way one obtains a unifying graphbased formal language for data and metadata definition and manipulation. In particular, a formalized specification framework for heterogeneous multibase systems can be built. The approach is described with a number of examples and then precisely formalized. The main technical contribution is the development of alge...
K.: Specifying overlaps of heterogeneous models for global consistency checking
 In: First Int. Workshop on ModelDriven Interoperability, MDI’2010, ACM Press
, 2010
"... Abstract. Software development often involves a set of models defined in different metamodels, each model capturing a specific view of the system. We call this set a multimodel, and its elements partial or local models. Since partial models overlap, they may be consistent or inconsistent wrt. a set ..."
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Cited by 8 (5 self)
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Abstract. Software development often involves a set of models defined in different metamodels, each model capturing a specific view of the system. We call this set a multimodel, and its elements partial or local models. Since partial models overlap, they may be consistent or inconsistent wrt. a set of global constraints. We present a framework for specifying overlaps between partial models and defining their global consistency. An advantage of the framework is that heterogeneous consistency checking is reduced to the homogeneous case yet merging partial metamodels into one global metamodel is not needed. We illustrate the framework with examples and sketch its formal
A Graphical Yet Formalized Framework for Specifying View Systems
, 1997
"... A graphical formalized language is proposed for specifying systems of views over database schemas. The language is based on the notion of arrow (mapping) between data schemas and is suitable for any data model for which schema mappings are defined. In particular, the constructs of query, query langu ..."
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Cited by 7 (6 self)
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A graphical formalized language is proposed for specifying systems of views over database schemas. The language is based on the notion of arrow (mapping) between data schemas and is suitable for any data model for which schema mappings are defined. In particular, the constructs of query, query language, view and view integration can be consistently expressed in this arrow formalism and correspondingly specified. This gives rise to a general graphbased framework for specifying complex view systems. Basic constructions of the language and the entire framework as well can be considered as specialization of very general constructs developed in the mathematical category theory. 1 Introduction The notion of view is one of the central ones in the database (DB) technology. Views make it possible to provide each application with its own presentation of data and isolate them from inessential (for them) details and changes of DB schemas. The practical importance of views is commonly recognized...
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
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 2 (2 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. ? Supported by Grants 93.315 and 96.0316 from the Latvian Council of Science ?? Supported partially by Grant 314/9472II (the scheme for research collaboration wit...
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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Cited by 2 (1 self)
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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...
Algebraic GraphBased Approach to Schema Integration
 In Databases and Information Systems, 2nd Int.Baltic Workshop
, 1996
"... The language of sketches is as concise and powerful as higher order logic and as handy as conventional ERdiagrams. We discuss its benefits in respect to problems of schema integration. It is evident that a chief property of the next generation information systems is their organization on cooperati ..."
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Cited by 1 (1 self)
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The language of sketches is as concise and powerful as higher order logic and as handy as conventional ERdiagrams. We discuss its benefits in respect to problems of schema integration. It is evident that a chief property of the next generation information systems is their organization on cooperative principles. Typically, applications involved in a cooperative system have to access data stored in several separate databases. These databases can be differently organized, semantically overlapping and even inconsistent, so that an application programmer encounters severe problems, moreover, in each multibase case they have to be solved specifically. In fact, as it was noted in [13], the situation is similar to the multifile situation before invention of DBs, and the analogous solution can be suggested: in order to provide applications with a single integral view of data, local DBs should be integrated into a united distributed DB. Under the latter we mean a database system which has a sc...
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...
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 int ..."
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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. ? Supported by Grants 93.315 and 96.0316 from the Latvian...