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Algebraic GraphOriented = Category Theory Based  Manifesto of categorizing database theory
, 1996
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Variable Sets and Functions Framework for Conceptual Modeling: Integrating ER and OO via Sketches with Dynamic Markers
 In OOER'95: ObjectOriented and EntityRelationship Modeling, Proc. 14th Int.Conf., Springer LNCS'1021
, 1995
"... . In the paper a graphbased specification language for semantic modeling is proposed. It is as handy as conventional graphical languages but, in contrast to them, possesses a precisely formalized semantics based on certain ideas of the mathematical category theory. In particular, it provides mathem ..."
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Cited by 18 (16 self)
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. In the paper a graphbased specification language for semantic modeling is proposed. It is as handy as conventional graphical languages but, in contrast to them, possesses a precisely formalized semantics based on certain ideas of the mathematical category theory. In particular, it provides mathematically correct semantics for formerly somewhat mythical notions of object identity and weak entity type. Among other benefits of the approach there are provable (!) universality w.r.to simulation of any other formal data specification, flexibility and unification in treating various kinds of associations and relationships, precise semantic basis for the familiar distinguishing between the specialization and generalization ISArelationships, intrinsic objectorientedness. 1 Introduction It appears that currently there are two central questions in the area of conceptual modeling and design: the first one is how to handle heterogeneity of semantic data models, and the second consists in inte...
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 15 (9 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...
EntityRelationshipAttribute Designs And Sketches
 Theory Appl. Categ
, 2002
"... EntityRelationshipAttribute ideas are commonly used to specify and design information systems. They use a graphical technique for displaying the objects of the system and relationships among them. The design process can be enhanced by specifying constraints of the system and the natural environmen ..."
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Cited by 14 (3 self)
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EntityRelationshipAttribute ideas are commonly used to specify and design information systems. They use a graphical technique for displaying the objects of the system and relationships 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, finitesum sketches with a terminal node are the appropriate class and call them EA sketches. A model for an EA sketch in a lextensive category is a `snapshot' of a database with values in that category. The category of models of an EA sketch is an object of models of the sketch in a 2category of lextensive categories. Moreover, modelling the same sketch in certain objects in other 2categories defines both the query language for the database and the updates (the dynamics) for the database. 1.
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 12 (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 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 12 (9 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...
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 11 (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...
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 10 (7 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...
Database Interoperability Through State Based Logical Data Independence
 INTERNATIONAL JOURNAL OF COMPUTER APPLICATIONS IN TECHNOLOGY
, 2000
"... Computer supported cooperative work (CSCW) involving businesstobusiness transactions depends more and more upon database interoperability. The design of interbusiness CSCW when the businesses are already operating independent systems depends either upon effective reverse engineering (to properly d ..."
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Cited by 9 (7 self)
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Computer supported cooperative work (CSCW) involving businesstobusiness transactions depends more and more upon database interoperability. The design of interbusiness CSCW when the businesses are already operating independent systems depends either upon effective reverse engineering (to properly discover the semantics underlying each organisation's systems and through that to develop appropriate matches for interbusiness software), or upon sufficiently rich semantic models and good database management system support for logical data independence (to allow database updating through a logical view). This paper takes the second approach presenting a rich semantic data model that the authors have been developing and have used successfully in a number of major consultancies, and a new approach to logical data independence and view updatability based on that model. We show how these approaches support database interoperability for businesstobusiness transactions, and, for CSCW within an organisation, how they support federated databases.
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 9 (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...