Table 1.

Name	Designation	Value
Tautology	P I	1
Controversy	P O	0
Negation	¬P	1 − P
Disjunction	P∨Q	$\left\{\begin{array}{cc}\frac{p+q}{\mathrm{2}},\hfill & p+q<\mathrm{1},\hfill \\ \mathrm{1},\hfill & p+q\ge \mathrm{1}\hfill \end{array}\right.$
Conjunction	P∧Q	$\left\{\begin{array}{cc}\frac{p+q}{\mathrm{2}},\hfill & p+q>\mathrm{1},\hfill \\ \mathrm{0},\hfill & p+q\le \mathrm{1}\hfill \end{array}\right.$
Implication	P → Q	$\left\{\begin{array}{cc}\frac{\mathrm{1}-p+q}{\mathrm{2}},\hfill & p>q,\hfill \\ \mathrm{1},\hfill & p\le q\hfill \end{array}\right.$
Equivalence	P↔Q	$\left\{\begin{array}{cc}\frac{\mathrm{1}-p+q}{\mathrm{2}},\hfill & p>q,\hfill \\ \mathrm{1},\hfill & p=q,\hfill \\ \frac{\mathrm{1}-q+p}{\mathrm{2}},\hfill & p<q\hfill \end{array}\right.$
Pierce arrow	P ↓ Q	$\left\{\begin{array}{cc}\mathrm{1}-\frac{p+q}{\mathrm{2}},\hfill & p+q<\mathrm{1},\hfill \\ \mathrm{0},\hfill & p+q\ge \mathrm{1}\hfill \end{array}\right.$
Shaffer stroke	P↑Q	$\left\{\begin{array}{cc}\mathrm{1}-\frac{p+q}{\mathrm{2}},\hfill & p+q>\mathrm{1},\hfill \\ \mathrm{1},\hfill & p+q\le \mathrm{1}\hfill \end{array}\right.$