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Facial action estimation from a single image is often formulated as predicting or fitting parameters in compact expression spaces, which lack explicit semantic interpretability. However, many practical applications, such as avatar control and human-computer interaction, require interpretable facial actions that correspond to meaningful muscle movements. In this work, we propose SemanticFace, a framework for facial action estimation in the interpretable ARKit blendshape space that reformulates coefficient prediction as structured semantic reasoning. SemanticFace adopts a two-stage semantic distillation paradigm: it first derives structured semantic supervision from ground-truth ARKit coefficients and then distills this knowledge into a multimodal large language model to predict interpretable facial action coefficients from images. Extensive experiments demonstrate that language-aligned semantic supervision improves both coefficient accuracy and perceptual consistency, while enabling strong cross-identity generalization and robustness to large domain shifts, including cartoon faces.