In Boolean functions and propositional calculus, the Sheffer stroke denotes a logical operation that is equivalent to the negation of the conjunction operation, expressed in ordinary language as "not both". It is also called non-conjunction, or alternative denial[1] (since it says in effect that at least one of its operands is false), or NAND ("not and").[1] In digital electronics, it corresponds to the NAND gate. It is named after Henry Maurice Sheffer and written as or as or as or as in Polish notation by Łukasiewicz (but not as ||, often used to represent disjunction).
Its dual is the NOR operator (also known as the Peirce arrow, Quine dagger or Webb operator). Like its dual, NAND can be used by itself, without any other logical operator, to constitute a logical formal system (making NAND functionally complete). This property makes the NAND gate crucial to modern digital electronics, including its use in computer processor design.
^ abHowson, Colin (1997). Logic with trees: an introduction to symbolic logic. London; New York: Routledge. p. 43. ISBN 978-0-415-13342-5.
In Boolean functions and propositional calculus, the Shefferstroke denotes a logical operation that is equivalent to the negation of the conjunction operation...
typography. It has many names, often related to particular meanings: Shefferstroke (in logic), pipe, bar, or (literally the word "or"), vbar, and others...
\operatorname {NOR} } . As with its dual, the NAND operator (also known as the Shefferstroke—symbolized as either ↑ {\displaystyle \uparrow } , ∣ {\displaystyle...
gates using NOR logic. Boolean algebra Flash memory Logic gate symbols Shefferstroke Mano, M. Morris and Charles R. Kime. Logic and Computer Design Fundamentals...
first published proof was by Henry M. Sheffer in 1913, so the NAND logical operation is sometimes called Shefferstroke; the logical NOR is sometimes called...
introduction of the Shefferstroke ("|") to symbolise "incompatibility" (i.e., if both elementary propositions p and q are true, their "stroke" p | q is false)...
structures and chip deposition geometries that produce NAND logic elements Shefferstroke – other name NOR logic. Like NAND gates, NOR gates are also universal...
A{\displaystyle A} ∴¬B{\displaystyle \therefore \neg B} Based on the ShefferStroke (alternative denial), "|", the inference can also be formalized in this...
recommended instead. ↑ | U+2191 U+007C upwards arrow vertical line Shefferstroke, the sign for the NAND operator (negation of conjunction). ↓ U+2193...
known as the Shefferstroke). It is one of 25 candidate axioms for this property identified by Stephen Wolfram, by enumerating the Sheffer identities of...
first published proof was by Henry M. Sheffer in 1913, so the NAND logical operation is sometimes called Shefferstroke; the logical NOR is sometimes called...
{\displaystyle {\frac {A,\neg \left(A\wedge \neg B\right)}{B}}} Because Sheffer'sstroke (also known as NAND operator) is functionally complete, it can be used...
negation, or even using only a single connective for "not and" (the Shefferstroke), as Jean Nicod did. A joint denial connective (logical NOR) will also...
terms of a sole sufficient operator such as the Peirce arrow (NOR) or Shefferstroke (NAND). Similarly, in classical first-order logic, one of the quantifiers...
Minimal axioms for Boolean algebra Peirce arrow Read-once function Shefferstroke Sole sufficient operator Symmetric Boolean function Symmetric difference...
equations yet further; for instance, with the vertical bar representing the Shefferstroke operation, the single axiom ( ( a ∣ b ) ∣ c ) ∣ ( a ∣ ( ( a ∣ c ) ∣...
first published proof was by Henry M. Sheffer in 1913, so the NAND logical operation is sometimes called Shefferstroke; the logical NOR is sometimes called...
of its inputs is true and the other is false ("not equal") NAND or Shefferstroke - true when it is not the case that all inputs are true ("not both")...
same cardinality stretch A convex subclass of an ordered class stroke The Shefferstroke (only used in the second edition of PM) type As in type theory...
first published proof was by Henry M. Sheffer in 1913, so the NAND logical operation is sometimes called Shefferstroke; the logical NOR is sometimes called...
innovations are introduced. For Quine, there is but one connective, the Shefferstroke, and one quantifier, the universal quantifier. All polyadic predicates...
as well. In his 4.3 through 5.101, Wittgenstein adopts an unbounded Shefferstroke as his fundamental logical entity and then lists all 16 functions of...
algebra are in common use, the lattice basis, the ring basis, and the Shefferstroke or NAND basis. These bases impart respectively a logical, an arithmetical...
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