I'm a lay mathematician adding a spoonful of logic in my math diet but I'm having trouble cracking the naming conventions. In particular it is difficult to search on line for more information with such compact sometimes cryptic naming conventions and I'm in search of the way to properly decode the names.
I am sure there are no strict rules but I'm interested in even a rough pattern. So far I have gleaned there seem to be three parts, for this post I will denote them $$ \alpha\beta\cdots - \mathrm{ABC}\cdots_{\to\&\vee\cdot} $$
The examples below are found in
Mints, Grigori, A short introduction to intuitionistic logic, The University Series in Mathematics. New York, NY: Kluwer Academic/Plenum Publishers (ISBN 0-306-46394-6/hbk). ix, 131 p. (2000). ZBL1036.03003.
Hindley, J. Roger; Seldin, Jonathan P., Introduction to combinators and (\lambda)-calculus, London Mathematical Society Student Texts, 1. Cambridge etc.: Cambridge University Press. VIII, 360 p. (1986). ZBL0614.03014.
Things in Greek before the hyphen seem to be intro/elim rules, e.g. $\lambda$, or $\beta\eta$-.
Question 1: Is there a fixed and agreed to list of what is permitted for the Greek letters to indicate. E.g. $\alpha,\beta,\eta$ seem to have agreed to meanings ($\alpha$ always for variable renaming, $\beta$ for reducing to normal form by eliminating $\lambda$'s), ($\eta$...less clear, seems there are several possible extentionality rules to choose from, so is $\eta$ a fixed one or just short for "author's favorite extensionality rules")? And should some other Greek letters be in that list?
Roman, the roman letters seem to name the logic, e.g. $LK$ for "Logic Klassic", $CL$ for "Combinatorial Logic", or some variations of that. But there are other letter combos that come in what seems like a pattern, $K$ replaced with $J$, $L$ with $N$, e.g. $NK, NJ,NL, NK$. A lot of combinations end in $C$, e.g. in $IQC$. And sometimes there is an upper vs. lower case letter, e.g. $NJp$, or $CLw$.
Question 2. Is there codex of what letters mean? Why the mixed case?
Lastly the symbols. These appear in places like $TA_{\lambda=}^{\to}$.
Question 3. What is communicated by the symbols as opposed to a rule like $\eta$ or a letter like $p$?
[Edited thanks to helpful community suggestions.]
