Logical Connectives - Common Logical Connectives - History of Notations

History of Notations

• Negation: the symbol ¬ appeared in Heyting in 1929. (compare to Frege's symbol in his Begriffsschrift); the symbol ~ appeared in Russell in 1908; an alternative notation is to add an horizontal line on top of the formula, as in ; another alternative notation is to use a prime symbol as in P'.
• Conjunction: the symbol ∧ appeared in Heyting in 1929 (compare to Peano's use of the set-theoretic notation of intersection ∩ ); & appeared at least in Schönfinkel in 1924; . comes from Boole's interpretation of logic as an elementary algebra.
• Disjunction: the symbol ∨ appeared in Russell in 1908 (compare to Peano's use of the set-theoretic notation of union ∪); the symbol + is also used, in spite of the ambiguity coming from the fact that the + of ordinary elementary algebra is an exclusive or when interpreted logically in a two-element ring; punctually in the history a + together with a dot in the lower right corner has been used by Peirce,
• Implication: the symbol → can be seen in Hilbert in 1917; ⊃ was used by Russell in 1908 (compare to Peano's inverted C notation); was used in Vax.
• Biconditional: the symbol ≡ was used at least by Russell in 1908; ↔ was used at least by Tarski in 1940; ⇔ was used in Vax; other symbols appeared punctually in the history such as ⊃⊂ in Gentzen, ~ in Schönfinkel or ⊂⊃ in Chazal.
• True: the symbol 1 comes from Boole's interpretation of logic as an elementary algebra over the two-element Boolean algebra; other notations include to be found in Peano.
• False: the symbol 0 comes also from Boole's interpretation of logic as a ring; other notations include to be found in Peano.

Some authors used letters for connectives at some time of the history: u. for conjunction (German's "und" for "and") and o. for disjunction (German's "oder" for "or") in earlier works by Hilbert (1904); Np for negation, Kpq for conjunction, Apq for disjunction, Cpq for implication, Epq for biconditional in Łukasiewicz (1929).