A Boolean model is a simple, discrete and dynamic model without the need to consider the effects at the intermediate levels. However, little effort has been made into constructing activation, inhibition, and protein decay networks, which could indicate the direct roles of a gene (or its synthesized protein) as an activator or inhibitor of a target gene. Therefore, we propose to focus on the general Boolean functions at the subfunction level taking into account the effectiveness of protein decay, and further split the subfunctions into the activation and inhibition domains. As a consequence, we developed a novel data-driven Boolean model; namely, the Fundamental Boolean Model (FBM), to draw insights into gene activation, inhibition, and protein decay. This novel Boolean model provides an intuitive definition of activation and inhibition pathways and includes mechanisms to handle protein decay issues. To prove the concept of the novel model, we implemented a platform using R language, called FBNNet. Our experimental results show that the proposed FBM could explicitly display the internal connections of the mammalian cell cycle between genes separated into the connection types of activation, inhibition and protein decay. Moreover, the method we proposed to infer the gene regulatory networks for the novel Boolean model can be run in parallel and; hence, the computation cost is affordable. Finally, the novel Boolean model and related Fundamental Boolean Networks (FBNs) could show significant trajectories in genes to reveal how genes regulated each other over a given period. This new feature could facilitate further research on drug interventions to detect the side effects of a newly-proposed drug.