Existing class-incremental learning methods struggle in multi-label scenarios (MLCIL) due to the inherent contradiction of learning objectives arising from co-occurring and incomplete labels. We argue that the core obstacle is the model's ambiguous boundary between known and unknown knowledge, which undermines historical knowledge retention, complicates current task learning, and limits adaptability to future concepts. To address this, we propose KBK (Knowing Beyond the Known), a reinforced knowledge specification framework that explicitly models what is known or not to unify historical, current, and prospective learning. Specifically, to clarify known knowledge, we develop a hierarchical feature purification module that disentangles fine-grained class-specific features from global features, where high-level semantic abstraction is reinforced with low-level visual features. Additionally, an uncertainty-aware recall enhancement strategy suppresses unreliable predictions based on distribution priors, improving the quality of historical recall. For probing the unknown, KBK leverages semantic correlations to synthesize informative unknown features under co-occurring, preserving embedding space for future learning. Furthermore, to mitigate heterogeneous forgetting, we design a category-balanced gradient compensation loss that dynamically reweights gradient backpropagation according to forgetting speeds. Experiments on multiple benchmarks validate the effectiveness and robustness of KBK, which surpasses prior best methods by 2.7% in Avg. Acc on MS-COCO B0-C10 setting even without any replay buffers.

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