Name

Designation

Value

Tautology

$\text{}A$ ^I

1

Controversy

$\text{}A$ ^O

0

Negation

$\neg A$

$\text{}1-A$

Disjunction

$A\vee B$

$\{\begin{array}{l}a\cdot b,a+b<1,\\ 1,a+b\ge 1\end{array}$

Conjunction

$A\wedge B$

$\{\begin{array}{l}a\cdot b,a+b>1,\\ 0,a+b\le 1\end{array}$

Implication

$A\to B$

$\{\begin{array}{l}\left(1-a\right)\cdot b,a>b,\\ 1,a\le b\end{array}$

Equivalence

$\text{}A\leftrightarrow B$

$\{\begin{array}{l}\left(1-a\right)\cdot b,a<b,\\ 1,a=b\\ \left(1-b\right)\cdot a,b<a,\end{array}$

Pierce Arrow

$A\downarrow B$

$\{\begin{array}{l}\left(1-a\right)\cdot \left(1-b\right),a+b<1,\\ 0,a+b\ge 1\end{array}$

Shaffer Stroke

$A\uparrow B$

$\{\begin{array}{l}\left(1-a\right)\cdot \left(1-b\right),a+b>1,\\ 1,a+b\le 1\end{array}$