Abstract
Certain second-order sentences, called conditional implicational dependencies, about relations in a relational database, are denned and studied. These dependencies include some of previously defined dependencies as special cases. Thus, the family of implicational dependencies introduced and studied by R. Fagip can be included in the family of conditional implicational dependencies. The conditional-functional dependencies defined by P. De Bra and J. Paredaens are special cases of new dependencies. A characterization of a conditional implicational dependency implied by a given class in this family, is given. The existence of Armstrong models for the class of conditional implicational dependencies with a single relational constant symbol is shown.
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