This paper presents a set of cognitive logics that capture the dynamics of knowledge acquisition and forgetting while incorporating the concept of collective knowledge. Based on a weighted model system, we introduce a "cognitive skill" measure that represents the cognitive ability associated with knowledge updating. Within this framework, knowledge acquisition is modeled as a process of skill enhancement, while forgetting is a consequence of skill degradation. Furthermore, we explore "knowability" and "forgetability," defined as the likelihood of knowledge acquisition through skill enhancement and the likelihood of forgetting through skill degradation, respectively. Furthermore, we provide a detailed analysis of the difference between cognitive de re and de dicto representations. We examine the computational complexity of model validation and the satisfiability problem, providing insights into the theoretical foundations and practical implications.