Peirce arrow

A two-place logical operation, usually denoted by $\downarrow$, specified by the following truth table:

$A$	$B$	$A\downarrow B$
$T$	$T$	$F$
$T$	$F$	$F$
$F$	$T$	$F$
$F$	$F$	$T$

Therefore, the statement $A\downarrow B$ denotes "neither A nor B". Peirce's arrow has the property that all logical operations can be expressed in terms of it. For example, the statement $\neg A$ (the negation of $A$) is equivalent to the statement $A\downarrow A$, while the conjunction $A\&B$ of two statements $A$ and $B$ is expressed as $(A\downarrow A)\downarrow(B\downarrow B)$ and the disjunction $A\lor B$ is equivalent to $(A\downarrow B)\downarrow(A\downarrow B)$. This arrow was introduced by C. Peirce.

Comments

A more familiar two-place logical operation in terms of which all others can be expressed is the so-called Sheffer stroke "AB": either $A$ or $B$ but not both. The Peirce arrow and the Sheffer stroke are each other negations.

References

[a1]	S.C. Kleene, "Introduction to metamathematics" , North-Holland (1950) pp. 139