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The stroke is named after Henry Maurice Sheffer, who in 1913 published a paper in the Transactions of the American Mathematical Society [10] providing an axiomatization of Boolean algebras using the stroke, and proved its equivalence to a standard formulation thereof by Huntington employing the familiar operators of propositional logic (AND, OR, NOT).
For example, an axiom with six NAND operations and three variables is equivalent to Boolean algebra: [1] (()) ((())) = where the vertical bar represents the NAND logical operation (also known as the Sheffer stroke).
In Boolean logic, logical NOR, [1] non-disjunction, or joint denial [1] is a truth-functional operator which produces a result that is the negation of logical or.That is, a sentence of the form (p NOR q) is true precisely when neither p nor q is true—i.e. when both p and q are false.
In that book, on p. 294, he gives the *incorrect* definition (the "NAND" definition) but actually claims that it comes from Sheffer's original paper, which Curry cites. This illustrates that at least one "authoritative" author really believes he is quoting Sheffer's original paper with this incorrect definition.
NAND or Sheffer stroke - true when it is not the case that all inputs are true ("not both") NOR or logical nor - true when none of the inputs are true ("neither") XNOR or logical equality - true when both inputs are the same ("equal") An example of a more complicated function is the majority function (of an odd number of inputs).
As shown by Alexander V. Kuznetsov, either of the following connectives – the first one ternary, the second one quinary – is by itself functionally complete: either one can serve the role of a sole sufficient operator for intuitionistic propositional logic, thus forming an analog of the Sheffer stroke from classical propositional logic: [6]
The first published proof was by Henry M. Sheffer in 1913, so the NAND logical operation is sometimes called Sheffer stroke; the logical NOR is sometimes called Peirce's arrow. [38] Consequently, these gates are sometimes called universal logic gates. [39] Eventually, vacuum tubes replaced relays for logic operations.
Sheffer was a Polish Jew born in the western Ukraine, who immigrated to the USA in 1892 with his parents and six siblings.He studied at the Boston Latin School before entering Harvard University, learning logic from Josiah Royce, and completing his undergraduate degree in 1905, his master's in 1907, and his Ph.D. in philosophy in 1908.