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).

Read more about this topic:  Logical Connectives, Common Logical Connectives

Other articles related to "history, history of":

Spain - History - Fall of Muslim Rule and Unification
... The breakup of Al-Andalus into the competing taifa kingdoms helped the long embattled Iberian Christian kingdoms gain the initiative ... The capture of the strategically central city of Toledo in 1085 marked a significant shift in the balance of power in favour of the Christian kingdoms ...
Xia Dynasty - Modern Skepticism
... The Skeptical School of early Chinese history, started by Gu Jiegang in the 1920s, was the first group of scholars within China to seriously question the traditional ... early Chinese history is a tale told and retold for generations, during which new elements were added to the front end" ...
History of Computing
... The history of computing is longer than the history of computing hardware and modern computing technology and includes the history of methods intended for pen and paper or for chalk and slate, with or ...
Casino - History of Gambling Houses
... form or another has been seen in almost every society in history ... From the Ancient Greeks and Romans to Napoleon's France and Elizabethan England, much of history is filled with stories of entertainment based on games of chance ... In American history, early gambling establishments were known as saloons ...
Voltaire - Works - Historical
... History of Charles XII, King of Sweden (1731) The Age of Louis XIV (1751) The Age of Louis XV (1746–1752) Annals of the Empire – Charlemagne, A.D ... II (1754) Essay on the Manners of Nations (or 'Universal History') (1756) History of the Russian Empire Under Peter the Great (Vol ... II 1763) History of the Parliament of Paris (1769) ...

Famous quotes containing the words history of and/or history:

    Indeed, the Englishman’s history of New England commences only when it ceases to be New France.
    Henry David Thoreau (1817–1862)

    At present cats have more purchasing power and influence than the poor of this planet. Accidents of geography and colonial history should no longer determine who gets the fish.
    Derek Wall (b. 1965)