On the Family of Conditional Embedded Implicational Dependencies

Abstract

Certain second-order sentences, called conditional embedded implicational dependencies, about relations in a relational database, are defined and studied. This class of dependencies includes some of previously defined dependencies as special cases. Thus, the family of implicational embedded dependencies introduced and studied by R. Fagin can be included in the family of conditional embedded implicational dependencies. The conditional-functional dependencies defined by P. De Bra and J. Paredaens are special cases of new dependencies. The family of conditional embedded implicational dependencies, also contains the family of conditional implicational dependencies, defined by the author. A characterization of a conditional embedded implicational dependency implied by a given class in this family is given. The existence of Armstrong models for a class of conditional embedded implicational dependencies with a single relational symbol is shown. CR categories: 4.33, 5.21, 5.27, 5.32

Keywords

• Armstrong relations
• functional dependency
• conditional dependency
• conditional implicational dependency
• implicational dependency
• conditional embedded implicational dependency
• relational database
• logical consequence
• mathematical logic