Abstract

In spite of the existence of many examples of incomplete logics, it is an important problem to find intermediate predicate logics complete with respect to Kripke frame (or Kripke sheaf) semantics because they are closed under substitution. But, most of known completeness proofs of finitely axiomatizable logics are difficult to apply to other logics since they are highly dependent on the specific properties of given logics. So, it is preferable to find a general methods of completeness proof. We give some results on this problem using canonical formulas of "propositional" logics 8,2ESS