Sheffer stroke

The Sheffersche line (also Sheffer stroke, Sheffer function Sheffer operator or English Sheffer stroke, named after Henry Maurice Sheffer ) and NAND (English and not = not and ) written as "|" referred to in the Boolean algebra and propositional logic a Boolean operator or connective.

The thus established logical operation is equivalent to the negation of the conjunction ( AND) of two boolean variables, colloquially " not both " this corresponds to.

Definition

Semantic Definition ( truth table )

The Sheffersche line denoted by "|" ( or sometimes called "↑ ", " NAND ", ""), is a two connective of propositional logic that is semantically defined by the following truth table (where t stands for true, f for wrong):

The overall presentation of two linked by the Shefferschen line statements is true if at least one statement is false, then false or if both are true.

Syntactic definition

The Sheffersche line can be defined by the negation of the conjunction:

History

The Sheffersche line is named after Henry Maurice Sheffer, who proved that the usual connectives of propositional logic, namely negation, conjunction, disjunction, conditional can be expressed by him etc.. Charles Sanders Peirce had this fact found more than thirty years ago, but never released. Peirce also realized that all connectives can be also through the 'dual' to Shefferschen line operator that Peirce function, NOR, express.

Equivalences

The usual connectives of propositional logic can be expressed as follows by the Shefferschen line:

Attributes and special features

The Sheffersche line has the peculiarity that he, alone forms without a further logical operators for propositional logic functionally complete Junktorensystem. This property is the basis for the importance of the NAND in the modern digital electronics.

The NAND and all other logical operations can be implemented by NAND gates respectively and their interconnection are in digital technology, therefore, as a standard block. In addition, NAND devices are often used because they are the best digital components. So as memory devices such as NAND flashes from NAND blocks are built up very little space.