Hybrid extensions of the minimal logic

We consider some extensions of Johansson's minimal logic J. Hybrid logics extend the intersection of the intuitionistic logic Int and the negative logic Neg. We show that the perceptibility and recognizability of a hybrid logic are reduced to the analogous properties of its intuitionistic and negative counterparts. Also, the interpolation properties of a hybrid logic are reduced to those of its intuitionistic and negative counterparts. The restricted interpolation property IPR and the projective Beth property PBP are known to be equivalent in the well-composed logics. Here we give an easier proof of this fact for hybrid logics.