Recursion theorem in Boolean valued propositional logic

Question

My question is quite simple: is Boolean valued prop logic a special case of the recursion theorem?
So, we have a finite set of propositional variables, inductive set of formulas constructed by some functions $f$ and $g$. Then, we have $B= \{0,1\}$ and Boolean function $h$ from $B^n$ to $B$ and assignment function $v$ from Var to $B$ and from Fm to $B$. Finally, $v(f(a,b))= h(v(a),v(b))$.
For example $v(-a)= 1-v(a)$. So, in some way, Boolean function recursively realizes logical formulas, doesn't it? I apologize very much for not using notation and perhaps not expressing myself clearly enough.