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Sheffer stroke

From Encyclopedia of Mathematics
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Sheffer bar

A logical operation, usually denoted by , given by the following truth table:'

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

Thus, the assertion means that and are incompatible, i.e. are not true simultaneously. All other logical operations can be expressed by the Sheffer stroke. For example, the assertion (the negation of ) is equivalent to the assertion ; the disjunction of two assertions and is expressed as:

The conjunction and the implication are expressed as and , respectively. Sheffer's stroke was first considered by H. Sheffer.

References

[1] H.M. Sheffer, "A set of five independent postulates for Boolean algebras, with applications to logical constants" Trans. Amer. Math. Soc. , 14 (1913) pp. 481–488


Comments

The Sheffer stroke operation is also called alternative denial.

References

[a1] S.C. Kleene, "Introduction to metamathematics" , North-Holland (1950) pp. 139
[a2] W. Marek, J. Onyszkiewicz, "Elements of logic and the foundations of mathematics in problems" , Reidel & PWN (1982) pp. 4
How to Cite This Entry:
Sheffer stroke. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Sheffer_stroke&oldid=16985
This article was adapted from an original article by V.E. Plisko (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article