Abstract

The authors of [MOC 00] conjectured that intuitionistic and classical logics are asymptotically identical. Their conjecture concerns the implicational parts of these logics over k variables and is trivially true for k = 1, because implicational parts of intuitionistic and classical logics over one variable are identical. So, it seems to be interesting to investigate the appropriate fragments of these logics for k = 2. The result is obtained by reducing the problem to the same one of Dummett's intermediate linear logic of two variables. Actually, this paper shows the existence of the density of this logic and demonstrates that the linear calculus covers a substantial part of classical propositional one.