Boolean networks (BNs) are systems of entities described by Boolean variables providing interaction in discrete time. They are particularly used in the modeling of Cell Signaling called Boolean Genetic Regulation Networks (BGRN). We present in this article a new representation of BGNR. For this representation, we use a modal Hypothesis Logic (H). We also introduce a representation for BNs in H which drives to new formal results. Our results make it possible to discriminate between stable configurations, limit cycles and unstable cycles of BNs. Ghost Extensions, defined in H, play here a key role.