12,089
edits
Changes
→Axioms: format displays as <math> arrays
|}
|}
One way of assigning logical meaning to the initial equations is known as the ''entitative interpretation'' (EN). Under EN, the axioms read as follows:
{| align="center" cellpadding="4" style="width:80%"
{| align="center" border="0" cellpadding="10"
| style="width:10%" | I<sub>1</sub>
|
<math>\begin{array}{ccccc}
I_1 & : &
\operatorname{true}\ \operatorname{or}\ \operatorname{true} & = &
\operatorname{true} \\
I_2 & : &
\operatorname{not}\ \operatorname{true}\ & = &
\operatorname{false} \\
J_1 & : &
a\ \operatorname{or}\ \operatorname{not}\ a & = &
\operatorname{true} \\
J_2 & : &
(a\ \operatorname{or}\ b)\ \operatorname{and}\ (a\ \operatorname{or}\ c) & = &
a\ \operatorname{or}\ (b\ \operatorname{and}\ c) \\
\end{array}</math>
|}
|}
Another way of assigning logical meaning to the initial equations is known as the ''existential interpretation'' (EX). Under EX, the axioms read as follows:
{| align="center" cellpadding="4" style="width:80%"
{| align="center" border="0" cellpadding="10"
| style="width:10%" | I<sub>1</sub>
|
<math>\begin{array}{ccccc}
I_1 & : &
\operatorname{false}\ \operatorname{and}\ \operatorname{false} & = &
\operatorname{false} \\
I_2 & : &
\operatorname{not}\ \operatorname{false} & = &
\operatorname{true} \\
J_1 & : &
a\ \operatorname{and}\ \operatorname{not}\ a & = &
\operatorname{false} \\
J_2 & : &
(a\ \operatorname{and}\ b)\ \operatorname{or}\ (a\ \operatorname{and}\ c) & = &
a\ \operatorname{and}\ (b\ \operatorname{or}\ c) \\
\end{array}</math>
|}
|}