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Abstract. The aim of the paper is discussion of connections between the three kinds of objects named in the title. In a sense, it is a survey of such connections; however, some new directions are also considered. This relates, especially, to sections 3, 4 and 5, where we consider a field that could be understood as an universal algebraic geometry. This geometry is parallel to universal algebra. In the monograph [51] algebraic logic was used for building up a model of a database. Later on, the structures arising there turned out to be useful for solving several problems from algebra. This is the position which the present paper is written from.

Abstract. We have systems rich in information but poor in knowledge. The paper shall sketch a framework in which information and knowledge could be properly integrated. Our initial hypothesis is that passing from information to knowledge involves the elaboration of a well structured theory of semiotic units. The latter is

The proposed principle of Interactive Databases (IDB) is intended to improve client-server interaction and to avoid database integrity constraints violation. In order to make the client more clever and give it the opportunity to make preliminary decisions regarding the correctness of the transactions without the server, we define the formal mechanism of "step-queries" definition. This mechanism is used as a tool for the conversion of the knowledge the DBMS has into the concrete collection of DML queries. Step-queries are used by the client. It sends them to the server before the transaction and the retrieves lists of possible values for the fields of the visual form. Then, these lists are used in order to give the user an opportunity to choose correct value for the given field. After the form has been completed the transaction could be filled with entered data. After the formal description of step-queries they must be mapped to DML. Here we will define the algorithm of such mapping int...

. 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-...

and Related Areas, sponsored by the Minerva Foundation (Germany)

In this paper we study the notion of knowledge from the positions of universal algebra and algebraic logic. We consider first order knowledge which is based on first order logic. We define categories of knowledge and knowledge bases. These notions are defined for the fixed subject of knowledge. The key notion of informational equivalence of two knowledge bases is introduced. We use the idea of equivalence of categories in this definition. We prove that for finite models there is a clear way to determine whether the knowledge bases are informationally equivalent.

Abstract. The paper is essentially a continuation of [PZ], whose main notion is that of logic-geometrical equivalence of algebras (LG-equivalence of algebras). This equivalence of algebras is stronger than elementary equivalence. In the paper we introduce the notion of isotyped algebras and relate it to LG-equivalence. We show that these notions coincide. The idea of the type is one of the central ideas in Model Theory. The correspondence introduced in the paper stimulates a bunch of problems which connect universal algebraic geometry and Model Theory. We provide a new general view on the subject, arising ”on the territory ” of universal algebraic geometry. This insight yields also applications of algebraic logic in Model Theory. Application of algebraic logic in Model theory makes some approaches more transparent. CONTENT