Boolean Dynamical Systems (BDS) are systems of entities described by Boolean variables providing interaction in discrete time. They are particularly used in the modeling of gene signaling pathways. We present new representations of BDSs and of gene regulation networks, using a modal non-monotonic logic (H) By using these representations every Boolean network can be represented by a set of modal formulas of H, and therefore by a set of Kripke models of H. The study of a BDS focuses in particular on the search of its stable configurations, limit cycles and unstable cycles. By using our representation, we prove that it is possible to discriminate between stable configurations, limit cycles and unstable cycles thanks to the introduction of a new concept, namely the ghost extensions. In addition the formalism introduced in this article uses a minimalist definition of the language of H, but sufficient to represent BNs. This restriction allows us to translate H into propositional calculus, hence to use SAT algorithms, and therefore to benefit of a simple and powerful implementation.