The combination of numerous simple influences between the components of a Biological Regulatory Network (BRN) often leads to behaviors that cannot be grasped intuitively. They thus call for the development of proper mathematical methods to delineate their dynamical properties. As a consequence , formal methods and computer tools for the modeling and simulation of BRNs become essential. Our recently introduced discrete formalism called the Process Hitting (PH), a restriction of synchronous automata networks, is notably suitable to such study. In this paper, we propose a new logical approach to perform model-checking of dynamical properties of BRNs modeled in PH. Our work here focuses on state reachability properties on the one hand, and on the identification of fixed points on the other hand. The originality of our model-checking approach relies in the exhaustive enumeration of all possible simulations verifying the dynamical properties thanks to the use of Answer Set Programming.