Abstract not found

Abstract not found

In the paper a new approach to semantic modeling and view integration is proposed. The underlying data model is graph-based yet completely formalized so that graphical schemas themselves are precise specifications suitable for implementation. The formalism is a kind of graph-object-based 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...

. 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 user-oriented 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...

. In the paper a new approach to semantic modeling and view integration is proposed. The underlying data model is graph-based 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 user-oriented schemas (views). Integration is called heterogeneous if local views are specified in different da...

. 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 graph-based 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 object-oriented and provides a quite natural way of specifying OO class-reference schemas. ffl Easy and f...

. A graph-based 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...

. 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 graph-based logic and algebra as opposed to string-based logics and algebras over sets currently employed in the DB theory. Such a graph-based 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 easy-to-...