The Problem of the Negation of the Conditional

People usually seem to negate the conditional in a different way as it is provided by standard logic. Both contemporary experimental results and texts coming from ancient sources appear to demonstrate that individuals tend not to negate the conditionals in entirety, but only their consequents. Obviously, this can lead one to think that there is no relationship between standard logic and human language and reasoning. However, in this paper, I try to show that, in spite of the mentioned results and texts, it is possible to continue to accept that there are certain links between systems such as that of Gentzen and the way people often negate the conditionals. That way is not, in many cases, exactly the one required by standard logic, but it is not absolutely inconsistent with the latter either.