Beyond the Black Box—A New Vector for Explainable AI Through Comparative Analysis of Logical Systems

Modern AI often works as a “black box”: it gives an answer, but cannot show why. In high-stakes fields like law, medicine, and government—and under emerging rules such as the EU AI Act—that is a serious problem. Today’s most popular explainability tools, such as SHAP and LIME, only approximate a model’s reasoning after the fact, and their explanations can be unstable. This review explores a different, often overlooked path: logical systems. We first explain in plain terms what they are and where they come from, then compare the main families—propositional, deontic, and first-order logic paired with modern solvers—by what each can express and guarantee. Our main contribution is a comparative taxonomy organized by explanatory guarantees, which reveals that no existing class simultaneously offers natural-language input, formal verifiability, and reproducibility. We then examine neuro-symbolic systems, illustrated by a representative engine (Causal Logic Engine, CLE), where a language model reads the text but a transparent logical layer makes the decision, checked by a human; the engine is described end to end, down to a worked example traced from raw text to the final decision. The key idea: instead of opening the black box, we move the decision outside it—so the reason behind every answer becomes clear and reproducible.