Results 1  10
of
14
Algebraic GraphBased Approach to Management of MultiBase Systems,II: Mathematical Aspects of Schema Integration
 TR9502, FRAME INFORM SYSTEMS
, 1995
"... ..."
Prototyping a Categorical Database in P/FDM
 In Second International Workshop on Advances in Databases and Information Systems ADBIS'95
, 1995
"... The relational data model uses set theory to provide a formal background, thus ensuring a rigorous mathematical data model with support for manipulation. The newer generation database models are based on the objectoriented programming paradigm, and so fall short of having a formal background, espe ..."
Abstract

Cited by 12 (2 self)
 Add to MetaCart
The relational data model uses set theory to provide a formal background, thus ensuring a rigorous mathematical data model with support for manipulation. The newer generation database models are based on the objectoriented programming paradigm, and so fall short of having a formal background, especially in some of the more complex data manipulation areas. We use category theory to provide a formalism for object databases, known as the product model. This paper will describe our formal model for the key aspects of object databases. In particular, we will examine how this model deals with three of the most important problems inherent in object databases, those of queries, closure and views. As well as this, we investigate the more common database concepts, such as keys, relationships, aggregation, etc. We will implement a prototype of this model using P/FDM, a semantic data model database system based on the functional model of Shipman, with objectoriented extensions. 1 Introduction ...
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 ..."
Abstract

Cited by 10 (9 self)
 Add to MetaCart
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, ..."
Abstract

Cited by 8 (5 self)
 Add to MetaCart
. 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...
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 ..."
Abstract

Cited by 7 (6 self)
 Add to MetaCart
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...
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 ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
. 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...
Comparison of Categorical Foundations of ObjectOriented Database Model
 In: Proceedings of 5th International Conference on Deductive and ObjectOriented Databases, Montreaux, CH
, 1997
"... . The present development in the database area is highly influenced by the objectoriented principles of data modeling. On the contrary to the previously successful relational approach, it lacks rigorous theoretical support. This problem is mainly due to the fact that the semantics description of su ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
. The present development in the database area is highly influenced by the objectoriented principles of data modeling. On the contrary to the previously successful relational approach, it lacks rigorous theoretical support. This problem is mainly due to the fact that the semantics description of such features as generalization, specialization, encapsulation, and inheritance is not trivial by using just the means of the set theory. Therefore, many researchers focused on finding suitable theoretical means for the modeling of complex objects. This paper is concerned with the comparison of categorical modeling in the database area and proposes a limit data model that enables to represent the objects, relationships, multiple inheritance, class polymorphism and virtual methods in the categorical setting. The aim to formalize these notions arose from the actual need. We would like to use it to support the development of an objectoriented database model closely following the standard ODMG'93...
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 ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
. 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...
Extending an ObjectOriented Model: Multiple Class Objects
, 1997
"... . Experiences of both researchers and practitioners with the development of objectoriented database systems help us to evaluate the real contributions of objectoriented modeling principles and show the limits and possibilities of improvements of the objectoriented model. One of the research areas ..."
Abstract
 Add to MetaCart
. Experiences of both researchers and practitioners with the development of objectoriented database systems help us to evaluate the real contributions of objectoriented modeling principles and show the limits and possibilities of improvements of the objectoriented model. One of the research areas where such a need was recognized concerns the class membership. In most objectoriented data model objects must belong to a single most specific class. However, the real world situations often break this presumption. The aim of this paper is to discuss the issues relating to an extension of modeling concepts to capture the objects that can belong to the multiple most specific classes. Our final objective is to present a framework for the formal objectoriented models that will provide the rigorous theoretical tool to solve issues concerning conflicts that can arise in structural components of objects. Most importantly, we show that the structural conflicts can be solved from the context det...
Data Modelling in Categorical and Computational Perspectives
, 1995
"... s people in their characterizations of the situation. Nevertheless, several main threads can be identified, and one of the most evident is that one depicted in the figure: computational procedures began to operate on extremely rich data structures while databases tend to be more flexible and involve ..."
Abstract
 Add to MetaCart
s people in their characterizations of the situation. Nevertheless, several main threads can be identified, and one of the most evident is that one depicted in the figure: computational procedures began to operate on extremely rich data structures while databases tend to be more flexible and involved from the computational view point. In fact, to manage modern distributed information systems effectively one is forced to think in terms of semantically valid computational procedures, while classical computations over classical ADTs should be moved to the level of implementation. Such a setting seems to be close to the paradigm of objectorientation which is actively inculcated in both programming and database technology as well. Figure 1. The evolution of information technologies (IT) As for the Theoryline and its relations to PL and DB, the picture we present is much more speculative. It appears that in computation