Idea on ‘implies’

I have a new thought.
There is no relation ‘implies’ (other than material implication) (between propositions).
Where one one wants to say F(a) strictly implies G(a).
One really has a relation SI(F,a,G,a)
S believes it would be
belief_r(S,t,’SI’,’F’,’a’,’G’,’a’) & symbol_r1(S,’SI’,Si) & symbol_r1(S,t,’F’,F), …..