Peirce arrow
From Encyclopedia of Mathematics
A two-place logical operation, usually denoted by 
, specified by the following truth table:'
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Therefore, the statement 
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 
(the negation of 
) is equivalent to the statement 
, while the conjunction 
of two statements 
and 
is expressed as 
and the disjunction 
is equivalent to 
. 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 
or 
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 |
How to Cite This Entry:
Peirce arrow. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Peirce_arrow&oldid=32867
Peirce arrow. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Peirce_arrow&oldid=32867
This article was adapted from an original article by V.E. Plisko (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article