Sheffer stroke

Sheffer stroke

In the late 19th century and early 20th century,

Charles Sanders Peirce

and H.M. Sheffer independently discovered that a single binary

logical connective

suffices to define all logical connectives (they are each

functionally complete

). Two such

connectives

are

•

↑

: the

Sheffer stroke

(sometimes denoted by

|

) and

•

↓

: the

Peirce arrow

(sometimes denoted by

⊥

).

The Sheffer stroke is defined by the

truth table

P

Q

P

↑

Q

F

F

T

F

T

T

T

F

T

T

T

F

O

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alternative denial

⁢

o

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⁢

NAND

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joint denial

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↑

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¬P := P↑P

.

W

e

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n

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∨

b

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P
∨
Q
:=

(
P
↑
P
)

↑

(
Q
↑
Q
)

,

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𝐑𝐞𝐦𝐚𝐫𝐤

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.

Title

Sheffer stroke

Canonical name

ShefferStroke

Date of creation

2013-03-22 18:51:55

Last modified on

2013-03-22 18:51:55

Owner

CWoo (3771)

Last modified by

CWoo (3771)

Numerical id

4

Author

CWoo (3771)

Entry type

Definition

Classification

msc 03B05

Synonym

alternative denial

Synonym

NAND

Synonym

joint denial

Synonym

NOR

Defines

Peirce arrow

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