Value Function

Assigns values to well-formed Propositional Logic formulas. It is recursively defined and uses the Interpretation Function to give meaning to the connectives and the Variable Assignment function to assign values to variables.

$$\begin{array}{rl}& {\mathcal{I}}_{\phi }(P)=\phi (P)\\ & {\mathcal{I}}_{\phi }(\neg \mathrm{A})=\mathcal{I}(\neg )\left({\mathcal{I}}_{\phi }(\mathrm{A})\right)\\ & {\mathcal{I}}_{\phi }(\mathrm{A}\wedge \mathrm{B})=\mathcal{I}(\wedge )\left({\mathcal{I}}_{\phi }(\mathrm{A}),{\mathcal{I}}_{\phi }(\mathrm{B})\right)\end{array}$$