Reasoning about dependencies in partial knowledge bases

In this paper we describe the rules for reasoning about existence dependencies and functional dependencies in partial knowledge bases. We characterize a formal system ED with only two rules for reasoning about existence dependencies. We prove that ED is sound and complete. In addition, we consider implication problem for functional dependencies. Three types of logical consequenses (implications) are described: standard, strong, and weak logical consequence. The center of our attention is the weak logical consequence and its properties. We prove that that reasoning based on the standard consequence is equivalent to reasoning based on the strong logical consequence, whereas reasoning based on the standard logical consequence and reasoning based on the strong logical consequence are not equivalent to reasoning based on the weak logical consequence..