Saturday, July 30, 2022
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A mnemonic from a course titled
“Galois Connections and Modal Logics“—
“Traditionally, there are two modalities, namely,
possibility and necessity. The basic modal operators
are usually written  (square) for necessarily
and  (diamond) for possibly.
Then, for example, P can be read as
‘it is possibly the case that P .'”
See also Intensional Semantics , lecture notes
by Kai von Fintel and Irene Heim, MIT,
Spring 2007 edition—
“The diamond ⋄ symbol for possibility is due to C.I. Lewis, first introduced in Lewis & Langford (1932), but he made no use of a symbol for the dual combination ¬⋄¬. The dual symbol □ was later devised by F.B. Fitch and first appeared in print in 1946 in a paper by his doctoral student Barcan (1946). See footnote 425 of Hughes & Cresswell (1968). Another notation one finds is L for necessity and M for possibility, the latter from the German möglich ‘possible.’”
Barcan, Ruth C.: 1946. “A Functional Calculus of First Order Based on Strict Implication.” Journal of Symbolic Logic, 11(1): 1–16. URL http://www.jstor.org/pss/2269159.
Hughes, G.E. & Cresswell, M.J.: 1968. An Introduction to Modal Logic. London: Methuen.
Lewis, Clarence Irving & Langford, Cooper Harold: 1932. Symbolic Logic. New York: Century.
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For less rigorous remarks, search Log24 for Modal Diamond Box.
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