In earlier work, Bancilhon and Spyratos introduced the concept of a complement to a database schema, and showed how this notion could be used in theories of decomposition and update semantics. However, they also showed that, except in trivial cases, even minimal complements are never unique, so that many desirable results, such as canonical decompositions, cannot be realized. Their work dealt with database schemata which are sets and database mappings which are functions, without further structure. In this work, we show that by adding a modest amount of additional structure, many important uniqueness results may be obtained. Specifically, we work with database schemata whose legal states form partially ordered sets (posets) with least elements, and with database mappings which are isotonic and which preserve this least element. This is a natural algebraic structure which is inherent in many important examples, including relational schemata constrained by data dependencies, with views constructed by composition of projection, restriction, and selection. Other examples include deductive database schemata in which views are defined by rules, and general first-order logic databases.

Database reformulation is the process of rewriting the data and rules of a deductive database in a functionally equivalent manner.

This paper addresses the problem of database schema design in the framework of the relational data model and functional dependencies. It suggests that both Third Normal Form (3NF) and BoyceCodd Normal Form (BCNF) supply an inadequate basis for relational schema design. The main problem with 3NF is that it is too forgiving and does not enforce the separation principle as strictly as it should. On the other hand, BCNF is incompatible with the principle of representation and prone to computational complexity. Thus a new normal form, which lies between these two and captures the salient qualities of both is proposed. The new normal form is stricter than 3NF, but it is still compatible with the representation principle. First a simpler definition of 3NF is derived, and the analogy of this new definition to the definition of BCNF is noted. This analogy is used to derive the new normal form. Finally, it is proved that Bernstein's algorithm for schema design synthesizes schemata that are already in the new normal form

Abstract: The notion of a functional relation among the attributes of a data set can be fruitfully applied in the structuring of an information system. These relations are meaningful both to the user of the system in his semantic understanding of the data, and to the designer in implementing the system. An important equivalence between operations with functional relations and operations with analogous Boolean functions is demonstrated in this paper. The equivalence is computationally helpful in exploring the properties of a given set of functional relations, as well as in the task of partitioning a data set into subfiles for efficient implementation. 1.

Abstract: An equivalence is shown between functional dependency statements of a relational database, where “+ ” has the meaning of “determines, ” and implicational statements of propositional logic, where “.$ ” has the meaning of “implies. ” Specifically, it is shown that a dependency statement is a consequence of a set of dependency statements iff the corresponding implicational statement is a con-sequence of the corresponding set of implicational statements. The database designer can take advantage of this equivalence to reduce problems of interest to him to simpler problems in propositional logic. A detailed algorithm is presented for such an application. Two proofs of the equivalence are presented: a “syntactic ” proof and a “semantic ” proof. The syntactic proof proceeds in several steps. It is shown that I) Armstrong’s Dependency Axioms are complete for dependency statements in the usual logical sense that they are strong enough to prove every consequence, and that 2) Armstrong’s Axioms are also complete for implicational statements in proposi-tional logic. The equivalence then follows from 1) and 2). The other proof proceeds by considering appropriate semantic interpreta-tions for the propositional variables. The Delobel-Casey Relational Database Decomposition Theorems, which heretofore have seemed somewhat fortuitous, are immediate and natural corollaries of the equivalence. Furthermore, a counterexample is demonstrat-ed, which shows that what seems to be a mild extension of the equivalence fails.

An algorithm is presented for designing relational views over network schemas to: (1) support general query and update capability, (2) preserve the information content of the data base and (3) provide independence from its physical organization. The proposed solution is applicable to many existing CCDASYL databases without data or schema conversion. The particular declarations of a CDDASYL schema which supply sources of logical data definition are first identified. Then the view design algorithm is derived on the basis of a formal analysis of the semantic constraints established by these declarations. A new form of data structure diagram is also introduced to visualize these constraints. 1. INTRczaltJcTIm This paper presents a rigorous solution to the problgn of designing relational views &ich support general wery and update capabilities over network schemas. Three objectives are of paramount concern in our approach. They are: 1. information preservation 2. updatability 3. data independence. Let us consider information preservation first. This is needed for supporting general purpose data manipulation capability. Indeed a user must be capable of accessing through views all the information of interest (within his authorization domain). Thus the view must be information-wise equivalent to the underlying schema or that portion of interest. Let us consider now the problem of specifying updates through a view (these include insert delete and modify operations). The simple data organization displayed by a view is often very Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial ad-vantage, the ACM copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Assooia-tion for Computing Machinery. To copy otherwise, or to republish, requires a fee end/or specific permission.

Object-oriented applications of database systems require database transformations involving non-standard functionalities such as set manipulation and object creation, i.e., the introduction of new domain elements. To deal with these functionalities, Abiteboul and Kanellakis introduced the "determinate" transformations as a generalization of the standard domain-preserving transformations. The obvious extensions of complete standard database programming languages, however, are not complete for the determinate transformations. To remedy this mismatch, the "constructive" transformations are proposed. It is shown that the constructive transformations are precisely the transformations that can be expressed in said extensions of complete standard languages. Thereto, a close correspondence between object creation and the construction of hereditarily finite sets is established. A restricted version of the main completeness result for the case where only list manipulations are involved is also ...

Conceptual modelling refers to the part of system development that involves investigating the problems and requirements of the users community and from that, developing a specification of the desired system. Conceptual modelling addresses two major aspects: the conceptual product (the so-called conceptual schema) and the conceptual process (the modelling process to deliver the conceptual product). Contributions to the field of conceptual modelling have emphasized the product aspect. A large variety of conceptual models have proposed high level concepts and abstraction mechanisms by which systems may be described at a conceptual level. Conceptual models have proved to be extremely useful throughout the information system life cycle and, hence, to be one of the most fundamental tools in the area of information systems engineering. However the growing demand for large and complex information systems calls for the introduction of new and more precise, formal techniques to model reality....

A “decompilation ” algorithm is developed to transform a program written with the procedural operations of CODASYL DML into one which interacts with a relational system via a nonprocedural query specification. An Access Path Model is introduced to interpret the semantic accesses performed by the program. Data flow analysis is used to determine how FIND operations implement semantic accesses. A sequence of these is mapped into a relational query and embedded into the original program. The class of programs for which the algorithm succeeds is characterized. Categories and Subject Descriptors: H.2.3 [Database Management]: Languages--data manipuh-tion languages (DML); query languages; CODACYL; H.2.5 [Database Management]: Heteroge-neous Databases-program translation

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