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.

Iφ(P)=φ(P)Iφ(¬A)=I(¬)(Iφ(A))Iφ(A∧B)=I(∧)(Iφ(A),Iφ(B))\begin{aligned} & \mathcal{I}_{\varphi}(P)=\varphi(P) \\ & \mathcal{I}_{\varphi}(\neg \mathrm{A})=\mathcal{I}(\neg)\left(\mathcal{I}_{\varphi}(\mathrm{A})\right) \\ & \mathcal{I}_{\varphi}(\mathrm{A} \wedge \mathrm{B})=\mathcal{I}(\wedge)\left(\mathcal{I}_{\varphi}(\mathrm{A}), \mathcal{I}_{\varphi}(\mathrm{B})\right) \end{aligned}