What exactly is the logical relation between the links in the twelvefold chain of Pratītyasamutpāda?
As I understand, the relationship is that of mutual implication. This meaning is reflected in the name pratitya-samutpada, that is often translated as "dependent co-arising" and such.

Mutual implication means one of the categories serves as context for the other and the other way around. Top is defined against bottom and vice verse. Life is defined against death and vice verse. This (upclose) is defined against That (far). Subjective is defined against Objective.

The twelve nidanas are meant to explain the emergence of the notion of Death by implication from Birth, of Birth by implication from Identifying with Separate Being, of Identifying with Separate Being by implication from Goal-making, of Goal-making by implication from Temporal Projection, of Temporal Projection by implication from Sensation as Result, of Sensation as Result by implication from Contact, of Contact by implication from Doors onto the world, of Doors onto the world by implication from Objects, of Objects by implication from Recognition, of Recognition by implication from Imprints, of Imprints by implication from Ignorance.