The first works (say, the constructive versions of Tarski's fixed point theorems by P. Cousot and R. Cousot) define a *prefix point* (alternately spelled as *prefixed point*, *fixed pre-point*, or *prefix*) of a card $ f colon X to X $ on a post $ (X, { le}) $ like a point $ x in X $ such as $ x le f (x) $. This use is continued today by the author (s) in, say, http://web.mit.edu/16.399/www/lecture_12-fixpoints2/Cousot_MIT_2005_Course_12_4-1.pdf and by their students. Twice, one *suffix point* (alternately spelled as *postfixed point*, *post-fixpoint*, or *postfixpoint*) is defined as a point $ x $ satisfactory $ f (x) le x $.

I could imagine that in case $ (X, { le}) $ is a complete network, *pre* points out that the prefix points are *Less* greater than or equal to the largest fixed point, and *Publish* points out that the suffix points are *bigger* greater than or equal to the lowest fixed point.

However, some authors have reversed it. If I get paraconsistent logic programming from Howard Arden Blair and Venkatramanan Siva Subrahmanian, Basic Category Theory for Computer Scientists from Benjamin Crawford Pierce, or even categories, types and data structures from Andréa Asperti and Giuseppe Longo, then the Usage is exactly the opposite. round: $ x $ is a *prefix point* so $ f (x) le x $, and $ x $ is a *suffix point* so $ x le f (x) $. I could imagine that *pre* underlines here the position of $ f $ to the *left* of the symbol of inequality, and *Publish* underlines the position of $ f $ to the *right* of the symbol of inequality.

There are dozens of research papers supporting either of the two conventions, but, to my knowledge, no early work (say ≤ 1979 for the first convention or ≤ 1987 for the second convention) that may be originally said *Why* they do so.

That said, are there any ideas as to why the discrepancy arose in the first place, or additional arguments or counter arguments in favor or against a particular naming convention? I hope that the authors of both conventions, whoever they are, have used the naming scheme by intuition and not by ignorance.