What is the origin of logical relations?
Plotkin used logical relations in his unpublished but nevertheless widely circulated and influential 1973 paper "Lambda Definability and Logical Relations". I have a copy of this note on my webpage.

I used to think that this is where the name came from, but when I asked Rick Statman about this, he told me that Mike Gordon coined the term logical relation to describe Tait's method, and that he and Gordon Plotkin picked it up from him. I think this is how it entered programming language jargon, though you could make sure by asking Plotkin.