The abstraction principle is
for K any formula not involving x. This is well known to be inconsistent and in  Hintikka proposed two modified versions of (0) which we briefly describe. First, he suggested
where K is any formula not involving x, and K+ is obtained from K by replacing subformulae of the form ∃zL by ∃z(z ≠ x ∧ L) and those of the form ∀zL by ∀z(z ≠ x → L), etc. The second version is
where K+ is a formula of the type described for (1) and z1 …, zk are all the free variables in (2).