I'm not sure what Z is supposed to be here. Sure some scientific hypotheses depend on prior hypotheses, which in turn depend on prior evidence. Of course the logical consequences of hypotheses are inherited by other hypotheses that depend on their truth, but that doesn't make scientific hypotheses any less empirical, or more formal, than they already are. You seem to be mixing them up here. You've lost kid-sib.
All barometer rises lead to rain falls.
Suppose that was really true. Today the barometer will rise. It follows logically that if H is true, rain will fall. That sounds like some sort of watered down Popperism, but it's simpler than that. Empirical truths can neither be proved true nor false with the force of logical necessity.