I’d say that A depends on B with respect to a property P(A) of A if a proof (logical reasoning) of why P(A) holds depends on an assumption about B; that is, if some property Q(B) of B is a necessary logical premise of the proof.
The article in its final definition of “dependence” talks about causation, but logical deduction (proof steps) seem more fundamental to me. It also talks about permissible changes, but the assumption that only permissible changes are talking place is just that, an assumption about the dependency.
The article in its final definition of “dependence” talks about causation, but logical deduction (proof steps) seem more fundamental to me. It also talks about permissible changes, but the assumption that only permissible changes are talking place is just that, an assumption about the dependency.