On the density of truth of implicational parts of intuitionistic and classical logics
Zofia Kostrzycka · Journal of Applied Non-Classical Logics · 2003
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 (see [DUM 54]). 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.