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Peirce arrow

From Encyclopedia of Mathematics
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A two-place logical operation, usually denoted by , specified by the following truth table:'

<tbody> </tbody>
T T F
T F F
F T F
F F T

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
This article was adapted from an original article by V.E. Plisko (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article