Incorporating record subtyping into a relational data model

Most of the current proposals for new data models support the construction of heterogeneous sets. One of the major challenges for such data models is to provide strong typing in the presence of heterogenity. Therefore the inclusion of as much as possible information concerning legal structural variants is needed. We argue that the shape of some part of a heterogeneous scheme is often determined by the contents of some other part of the scheme. This relationship can be formalized by a certain type of integrity constraint we have called attribute dependency. Attribute dependencies combine the expressive power of general sums with a notation that fits into relational models. We show that attribute dependencies can be used, besides their application in type and integrity checking, to incorporate record subtyping into a relational model. Moreover, the notion of attribute dependency yields a stronger assertion than the traditional record subtyping rule as it considers some refinements to be caused by others. To examine the differences between attribute dependencies and traditional record subtyping and to be able to predict how attribute dependencies behave under transformations like query language operations we develop an axiom system for their derivation and prove it to be sound and complete. We further investigate the interaction between functional and attribute dependencies and examine an extended axiom system capturing both forms of dependencies

Анализ типизированных зависимостей включения с неопределенными значениями

Null values have become an urgent problem since the creation of the relational data model. The impact of the uncertainty affects all types of dependencies used in the design and operation of the database. This fully applies to the inclusion dependencies, which are the theoretical basis for referential integrity on the data. Attempts to solve this problem contain inaccuracy in the statement of the problem and its solution. The errors in formulation of the problem can be associated with the use in the definition of untyped inclusion dependencies, which leads to permutations of the attributes, although, the attributes in database technology are identified by name and not by their place. In addition, linking with the use of the inclusion dependencies of heterogeneous attributes, even of the same type, is a sign of lost functional dependencies and leads to interaction of inclusion dependencies and non-trivial functional dependencies. Inaccuracies in the solution of the problem are contained in the statements of axioms and the proof of their properties, including completeness. In this paper we propose an original solution of this problem only for typed inclusion dependencies in the presence of Null values: a new axiom system is proposed, its completeness and soundness are proved. On the basis of inference rules we developed an algorithm for the construction of a not surplus set of typed inclusion dependencies. The correctness of the algorithm is proved.Неопределенные значения стали актуальной проблемой с момента создания реляционной модели данных. Влияние неопределенностей сказывается на всех видах зависимостей, используемых при проектировании и эксплуатации базы данных. В полной мере это относится и к зависимостям включения, которые являются теоретической основой ссылочной целостности на данные. Попытки решения указанной проблемы содержат неточности как в постановке задачи, так и в самом ее решении. К постановочным ошибкам можно отнести использование в определении нетипизированных зависимостей включения, что приводит к перестановкам атрибутов, хотя в технологиях баз данных атрибуты идентифицируются по имени, а не по их позиции. Кроме того, связывание зависимостью включения разнородных, пусть даже однотипных, атрибутов является признаком потерянной функциональной зависимости и приводит к взаимодействию нетривиальных зависимостей включения и функциональных зависимостей. Зависимости включения должны определять количественное соотнесение объектов друг с другом, а не значений атрибутов. Неточности в решении указанной проблемы содержатся в формулировках аксиом и доказательстве их свойств, в том числе полноты. В этой статье предлагается оригинальное решение этой проблемы только для типизированных зависимостей включения при наличии неопределенных значений: предложена система аксиом, доказана ее полнота и непротиворечивость. На основе правил вывода разработан алгоритм построения не избыточного множества типизированных зависимостей включения. Доказана корректность этого алгоритма

Guaranteeing no interaction between functional dependencies and tree-like inclusion dependencies

Functional dependencies (FDs) and inclusion dependencies (INDs) are the most fundamental integrity constraints that arise in practice in relational databases. A given set of FDs does not interact with a given set of INDs if logical implication of any FD can be determined solely by the given set of FDs, and logical implication of any IND can be determined solely by the given set of INDs. The set of tree-like INDs constitutes a useful subclass of INDs whose implication problem is polynomial time decidable. We exhibit a necessary and sufficient condition for a set of FDs and tree-like INDs not to interact; this condition can be tested in polynomial time

Justification for inclusion dependency normal form

Functional dependencies (FDs) and inclusion dependencies (INDs) are the most fundamental integrity constraints that arise in practice in relational databases. In this paper, we address the issue of normalization in the presence of FDs and INDs and, in particular, the semantic justification for Inclusion Dependency Normal Form (IDNF), a normal form which combines Boyce-Codd normal form with the restriction on the INDs that they be noncircular and key-based. We motivate and formalize three goals of database design in the presence of FDs and INDs: noninteraction between FDs and INDs, elimination of redundancy and update anomalies, and preservation of entity integrity. We show that, as for FDs, in the presence of INDs being free of redundancy is equivalent to being free of update anomalies. Then, for each of these properties, we derive equivalent syntactic conditions on the database design. Individually, each of these syntactic conditions is weaker than IDNF and the restriction that an FD not be embedded in the righthand side of an IND is common to three of the conditions. However, we also show that, for these three goals of database design to be satisfied simultaneously, IDNF is both a necessary and sufficient condition

On Independence Atoms and Keys

Uniqueness and independence are two fundamental properties of data. Their enforcement in database systems can lead to higher quality data, faster data service response time, better data-driven decision making and knowledge discovery from data. The applications can be effectively unlocked by providing efficient solutions to the underlying implication problems of keys and independence atoms. Indeed, for the sole class of keys and the sole class of independence atoms the associated finite and general implication problems coincide and enjoy simple axiomatizations. However, the situation changes drastically when keys and independence atoms are combined. We show that the finite and the general implication problems are already different for keys and unary independence atoms. Furthermore, we establish a finite axiomatization for the general implication problem, and show that the finite implication problem does not enjoy a k-ary axiomatization for any k