We introduce "argument-incomplete Abstract Argumentation Frameworks with dependencies", that extend the traditional abstract argumentation reasoning to the case where some arguments are uncertain and correlated through logical dependencies (such as mutual exclusion, implication, etc.). We characterize the complexities of the problems DSAT of deciding the satisfiability of the dependencies and PDVER of verifying extensions, and show how they depend on the forms of dependencies and, for PDVER, also on the semantics of the extensions.