I ask from the practitioner point-of-view, and I hope the answer does not come down to nit-picking, but I would like to settle the matter once and for all in the work I do.
One of the components of an Information Extraction (IE) pipeline is a relation(ship) extractor which picks out associations between entity mentions. Stanford CoreNLP talks about this extractor strictly using the term relation(s) extractor. Not that it is authoritative, but Wikipedia talks about relationship extraction. The former seems more prevalent based upon both code and papers I have come across. So is there an authoritative answer as to which is more proper, or are there legitimate cases to use both when talking about what we are trying to do?
