Future wireless networks are anticipated to support a wide range of human-centric intelligent services and applications that are data-intensive and resource-consuming, requiring low latency and high reliability. This motivates the adoption of a novel paradigm called semantic-aware communication, seen as a revolutionary approach with the potential to transform the design and operation of wireless communication systems. Optimization problems involving unmanned aerial vehicle (UAV) mobility and non-orthogonal multiple access (NOMA), where multiple symbols are simultaneously transmitted and detected, are particularly difficult due to their NP-hard nature. Furthermore, conventional communication networks have focused on accurate message reception without considering the semantic meaning of messages. Next-generation networks can be enriched by incorporating semantic, context-aware reasoning into their design. In this paper, our objective is to maximize the overall sum-rate performance by optimizing the power allocation based on UAV's mobility in a UAV-based NOMA network. Although classical optimization algorithms have shown impressive results over the years, their underlying complexity makes them difficult to implement in practical scenarios. Additionally, current machine learning models are limited to training results that do not leverage accumulated self-organized knowledge for future use, resulting in limited generalizability to new situations. To resolve these challenges, we propose a novel data-driven, semantic-aware framework called the Active Semantic Generalized Dynamic Bayesian Network (Active-SGDBN). The framework integrates expert knowledge (exhaustive search optimization), active inference (inspired by cognitive neuroscience), and semantic learning to develop a more intelligent, adaptable, and efficient resource allocation scheme. Simulation results have validated the effectiveness of the proposed approach in reaching a near-optimal solution and surpassing other benchmark schemes in terms of achievable sum rate.