Extended Truth Assignment

A function ${\tau }^{\ast }:\mathcal{F}\to \{0,1\}$

When evaluated, ${\tau }^{\ast }(x)=\tau (x)$

Properties

• ${\tau }^{\ast }(\neg p_1)=1-{\tau }^{\ast }(p_1)$
• ${\tau }^{\ast }((p_1\wedge p_2))={\tau }^{\ast }(p_1)\ast {\tau }^{\ast }(p_2)=min({\tau }^{\ast }(p_1),{\tau }^{\ast }(p_2))$
• ${\tau }^{\ast }(p_1\vee p_2)=max({\tau }^{\ast }(p_1),{\tau }^{\ast }(p_2))$

1 & \text{ if } \tau^(p_1) = 0 \text{ or } \tau^{}(p_{2}) = 1\ 0 & \text{ otherwise } \end{cases}$$

1 & \text{ if } \tau^(p_1) = \tau^{}(p_{2})\ 0 & \text{ otherwise } \end{cases}$$