Summary: It is shown, that a sufficiently large class of dependencies (“hypothesis-conclusion” type of dependencies) can be expressed as first-order sentences (HCD-formulas). In the second part we deal with implication problems, namely with the generalization of implication problems for TTGD, TGD, EGD types of dependencies, introduced by C. Beeri and M. Y. Vardi [J. Assoc. Comput. Mach. 31, 718-741 (1984; Zbl 0632.68097)]. For these implication problems we give a generalized version of the so called chase proof procedure. We introduce exchangeability - generating dependency (XGD) and analyze the structure of relation classes satisfying XGDs, from the point of view of invariant dependencies.