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18
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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View Updatability Based on the Models of a Formal Specification
, 2001
"... Information system software productivity can be increased by improving the maintainability and modifiability of the software produced. This latter in turn can be achieved by the provision of comprehensive support for views, since view support allows application programs to continue to operate un ..."
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Cited by 12 (8 self)
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Information system software productivity can be increased by improving the maintainability and modifiability of the software produced. This latter in turn can be achieved by the provision of comprehensive support for views, since view support allows application programs to continue to operate unchanged when the underlying information system is modified. But, supporting views depends upon a solution to the view update problem, and proposed solutions to date have only had limited, rather than comprehensive, applicability. This paper presents a new treatment of view updates for formally specified information systems. The formal specification technique we use is based on category theory and has been the basis of a number of successful major information system consultancies. We define view updates by a universal property in a subcategory of models of the formal specification, and explain why this indeed gives a comprehensive treatment of view updatability, including a solution to the view update problem. However, a definition of updatability which is based on models causes some inconvenience in applications, so we prove that in a variety of circumstances updatability is guaranteed independently of the current model. The paper is predominantly theoretical, as it develops the theoretical basis of a formal methods technique, but the methods described here are currently being used in a large consultancy for a government Department of Health. Because the application area, information systems, is rarely treated by formal methods, we include some detail about the formal methods used. In fact they are extensions of the usual category theoretic specification techniques, and the solution to the view update problem can be seen as requiring the existence of an...
View Updates in a Semantic Data Modelling Paradigm
 In ADC ’01: Proceedings of the 12th Australasian conference on Database technologies. IEEE Computer Society
, 2001
"... The Sketch Data Model (SkDM) is a new semantic modelling paradigm based on category theory (specifically on categorical universal algebra), which has been used successfully in several consultancies with major Australian companies. This paper describes the sketch data model and investigates the view ..."
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Cited by 9 (5 self)
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The Sketch Data Model (SkDM) is a new semantic modelling paradigm based on category theory (specifically on categorical universal algebra), which has been used successfully in several consultancies with major Australian companies. This paper describes the sketch data model and investigates the view update problem (VUP) in the sketch data model paradigm. It proposes an approach to the VUP in the SkDM, and presents a range of examples to illustrate the scope of the proposed technique. In common with previously proposed approaches, we define under what circumstances a view update can be propagated to the underlying database. Unlike many previously proposed approaches the definition is succinct and consistent, with no ad hoc exceptions, and the propagatable updates form a broad class. We argue that we avoid ad hoc exceptions by basing the definition of propagatable on the state of the underlying database. The examples demonstrate that under a range of circumstances a view schema can be shown to have propagatable views in all states, and thus stateindependence can frequently be recovered. Keywords: View update, category theory, data model, semantic data modelling 1
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...
Fibrations and universal view updatability
"... Maintainability and modifiability of information system software can be enhanced by the provision of comprehensive support for views, since view support allows application programs to continue to operate unchanged when the underlying information system is modified. Supporting views depends upon a so ..."
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Cited by 4 (1 self)
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Maintainability and modifiability of information system software can be enhanced by the provision of comprehensive support for views, since view support allows application programs to continue to operate unchanged when the underlying information system is modified. Supporting views depends upon a solution to the view update problem. This paper presents a new treatment of view updates for formally specified semantic data models based on the category theoretic sketch data model. The sketch data model has been the basis of a number of successful major information system consultancies. We define view updates by a universal property in models of the formal specification, and explain why this indeed gives a complete and correct treatment of view updatability, including a solution to the view update problem. However, a definition of updatability which is based on models causes some inconvenience in applications, so we prove that in a variety of circumstances updatability is guaranteed independently of the current model. This is done first with a very general criterion, and then for some specific cases relevant to applications. We include some detail about the sketch data model, noting that it involves extensions of algebraic data specification techniques.
Sketch Data Models, Relational Schema and Data Specifications
 ENTCS, Volume
, 2001
"... When different mathematical models are used for software analysis and development it is important to understand their relationships. When the models are truly mathematical, and when the aspects of reality that they seek to model are common, it may be possible to express their relationships in precis ..."
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Cited by 4 (3 self)
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When different mathematical models are used for software analysis and development it is important to understand their relationships. When the models are truly mathematical, and when the aspects of reality that they seek to model are common, it may be possible to express their relationships in precise mathematical terms. This paper studies three mathematical models: The sketch data model, the relational data model, and the data specifications of Piessens and Steegmans, and determines their relationships mathematically and in detail. The constructions presented here answer reasonably longstanding theoretical questions, and offer techniques that promise to be practically useful in integrating data models.
EntityRelationship Models and Sketches
, 1996
"... EntityRelationship models are a common tool for specification and design of information systems. They use a graphical technique for displaying the objects of the system and relatioships among them. The design process can be enhanced by specifying constraints of the system and the natural environmen ..."
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Cited by 2 (1 self)
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EntityRelationship models are a common tool for specification and design of information systems. They use a graphical technique for displaying the objects of the system and relatioships among them. The design process can be enhanced by specifying constraints of the system and the natural environment for these is the categorical notion of sketch. Here we argue that the finitelimit, finitecoproduct sketches with a terminal node are the appropriate class and call them ER sketches. A model for an ER sketch is a `snapshot' of a database. The models of an ER sketch in a lextensive category are a category with determined values on the entities and additional properties in case the entities have key attributes. Among the models is the query language associated to the ER sketch. We also show that database updates are simply spans of models. Moreover the category of updates of models of an ER sketch is the category of models of the sketch in the 2category of spans. Research partially supp...
Update Algorithms for the Sketch Data Model
 Proceedings of CSCWD 2001, the Sixth International Conference on Computer Supported Cooperative Work in Design, 367–376, NRC and IEEE
, 2001
"... The authors have developed a new approach to database interoperability using the sketch data model. That technique has now been used in a number of applications, but an important question remains: What are the algorithms that support updates in the sketch data model? The question has significant con ..."
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Cited by 2 (1 self)
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The authors have developed a new approach to database interoperability using the sketch data model. That technique has now been used in a number of applications, but an important question remains: What are the algorithms that support updates in the sketch data model? The question has significant content since the sketch data model uses EAsketches to specify data structures, and these include constraint and other information not normally supported by relational database management systems. In this paper we answer the question by using the framework of EA sketches to give a detailed mathematical treatment of database updates, providing a formal definition of insert update together with an algorithm which provably achieves updates. The algorithm is new as it is the first to treat data and constraints on an equal categorical footing. We also note that further exactness properties (limits and colimits) can aid specification, and we provide algorithms for updates of EA sketched databases with finite limits. These are the first update algorithms for such databases. The sketch data model is being used in industry for designing interoperations for computer supported cooperative workand computer assisted software engineering (CASE) tools are under development. The paper is predominantly theoretical, and provides an important link needed for CASE tool development. Keywords: Category theory, data model, mathematical specification, database interoperation 1.
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...