[FOM] FOM Formation Rules

[John Corcoran]

Edwin Mares asked: "Who was the first logician to present rigorous
formation rules for a formal language? And where (and when) did they do
it?"

No matter what is meant by rigorous this is an interesting question. I
would like to know when logicians started thinking of formal languages
as subsets of the set of finite strings over a finite alphabet, which of
course is what they are. My guess would include reference to Emil Post's
dissertation in the 1920's.
 
In order to make the original question precise one should specify more
fully what is mean by rigorous. If by rigorous you mean stated in a
formalized metalanguage having axioms characterizing the class of string
over the alphabet of the formal language in question, then the answer is
probably the Alfred Tarski 1933 truth-definition paper known as
"Wahrheitsbegriff" (references below). Unfortunately, it must be
admitted that Tarski seems to show no awareness of the essential
finiteness conditions.

Tarski, A.  1933.  The concept of truth in the languages of the
deductive sciences (Polish).  Prace Towarzystwa Naukowego Warszawskiego,
Wydzial III Nauk Matematyczno-Fizycznych 34, Warsaw; reprinted in
Zygmunt 1995, pages 13-172; expanded English translation in Tarski 1983,
pages 152-278.
Tarski, A. 1983.  Logic, Semantics, Metamathematics, papers from 1923 to
1938, Edited with introduction and analytic index by J. Corcoran,
Indianapolis: Hackett.
Zygmunt, J., Ed.  1995.  Alfred Tarski, Pisma Logiczno-Filozoficzne, 1
Prawda, Warsaw: Wydawnictwo Naukowe PWN.