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Causal discovery in time-series datasets is critical for understanding complex systems, especially when the \textit{effectiveness} of causal relationships depends on both the \textit{duration} and \textit{magnitude} of the cause. We introduce a novel framework for causal discovery based on \textbf{Signal Temporal Logic (STL)}, enabling the extraction of interpretable causal diagrams (STL-CD) that explicitly capture these temporal dynamics. Our method first identifies statistically meaningful time intervals, then infers STL formulas that classify system behaviors, and finally employs transfer entropy to determine direct causal relationships among the formulas. This approach not only uncovers causal structure but also identifies the temporal persistence required for causal influence—an insight missed by existing methods. Experimental results on synthetic and real-world datasets demonstrate that our method achieves superior structural accuracy over state-of-the-art baselines, providing more informative and temporally precise causal models.