Dependency types (Q2277841)

The paper aims at studying dependencies in a general setting thus providing a unified approach to some important structural problems in relational database theory. Several concepts and results introduced in connection with concrete dependencies are generalized in the presented framework of dependency types. The paper starts with formally introducing dependency types. The concepts of Armstrong relation and covers for dependency types are defined. The authors prove a necessary condition for a dependency type to have a k-ary sound and complete system of axioms. The problem of equivalence of axiom systems for dependency types is studied. The authors introduce a partial order on dependency types formalizing a `simpler than' order on dependency types. Based on this order, the reduction of dependency types to simpler ones is discussed. Finally, the authors formalize the concept of generalization of dependency types.