The 1955 manual for the IBM 704 on page 7 talks about data representation in the computer.
When a word is interpreted as numerical data, the
zero position acts as the sign of the word. (…) When
a logical operation is performed on a word, the
word is interpreted as a 32-bit signless number.
As an algebraic (signed) binary number, a word can
This is a little bit outside the scope of the question. It's not really arithmetic instructions (though they are common instructions, and some of them do involve arithmetic), and the architecture in question isn't very "retro". But anyway, maybe it will be of interest to someone.
In the ARMv8 architecture, circa 2011, most instructions write to ...
(Another "what was the first" question where it's basically impossible to answer it unless one goes through all computer instruction sets ...)
One example of the usage of "logical" is the IBM 7090 (1959), as one can verify in the manual where the shift instructions are listed starting on page 31:
ALS Accumulator Left Shift