Розширення UML специфікації для моделювання семантичних об’єктів

В статті запропоновано відображення діаграми класів UML до дескриптивної логіки діалекту SHOIQ. Запропоновано розширення нотацій UML, шляхом використання стереотипів, для максимального наближення семантичних конструкцій. Вказано на причини та проблеми що виникають при такому відображенні.В статье предложено отображения диаграммы классов UML в дескриптивную логику диалекта SHOIQ. Предложено расширение нотаций UML путем использования стереотипов, для максимального приближения семантических конструкций. Указано на причины и проблемы, которые возникают при таком отражении.In the article, propose mapping from UML class diagrams to SHOIQ. descriptive logic. Made approach through extension the UML notations by using stereotypes as close to semantic structures. Specified on the causes and problems that arise in such mapping

Keys and Armstrong databases in trees with restructuring

The definition of keys, antikeys, Armstrong-instances are extended to complex values in the presence of several constructors. These include tuple, list, set and a union constructor. Nested data structures are built using the various constructors in a tree-like fashion. The union constructor complicates all results and proofs significantly. The reason for this is that it comes along with non-trivial restructuring rules. Also, so-called counter attributes need to be introduced. It is shown that keys can be identified with closed sets of subattributes under a certain closure operator. Minimal keys correspond to closed sets minimal under set-wise containment. The existence of Armstrong databases for given minimal key systems is investigated. A sufficient condition is given and some necessary conditions are also exhibited. Weak keys can be obtained if functional dependency is replaced by weak functional dependency in the definition. It is shown, that this leads to the same concept. Strong keys are defined as principal ideals in the subattribute lattice. Characterization of antikeys for strong keys is given. Some numerical necessary conditions for the existence of Armstrong databases in case of degenerate keys are shown. This leads to the theory of bounded domain attributes. The complexity of the problem is shown through several examples

Weak functional dependencies on trees with restructuring

We present an axiomatisation for weak functional dependencies, i.e. disjunctions of functional dependencies, in the presence of several constructors for complex values. The investigated constructors capture records, sets, multisets, lists, disjoint union and optionality, i.e. the complex values are indeed trees. The constructors cover the gist of all complex value data models including object oriented databases and XML. Functional and weak functional dependencies are expressed on a lattice of subattributes, which even carries the structure of a Brouwer algebra as long as the union-constructor is absent. Its presence, however, complicates all results and proofs significantly. The reason for this is that the union-constructor causes non-trivial restructuring rules to hold. In particular, if either the set- or the the union-constructor is absent, a subset of the rules is complete for the implication of ordinary functional dependencies, while in the general case no finite axiomatisation for functional dependencies exists