Logic in Machine Learning and AI

Two Paths to AI: Symbolic and Connectionist

AI has developed according to two fundamentally different approaches. Symbolic AI (Good Old-Fashioned AI, GOFAI): represent knowledge in explicit logical form, write inference rules. “Expert systems” of the 1980s: a knowledge base of if-then rules + inference mechanism. Advantage: transparency, interpretability, precision in narrow domains. Limitation: “Brittleness” — fragility when going beyond the scope of the knowledge base.

Connectionist AI (neural networks): learning from data, without explicit rules. Advantage: flexibility, scalability, ability to find patterns in complex data. Limitation: “Black box” — lack of transparency, difficulty in interpretation.

Current trend: hybrids. “Neurosymbolic AI” — attempts to combine neural networks with symbolic reasoning. Google DeepMind AlphaCode — a neural network for programming, embedded into a symbolic system for correctness verification.

Logical Foundations of Machine Learning

Machine learning is statistical optimization, but with logical constraints. First-order logic allows us to set constraints: “If an X-ray shows a shadow — probability X is higher.” “Inductive logic programming” — learning logical rules from examples.

“Explainable AI” (XAI): regulators (EU AI Act) and ethics require decisions of AI to be explainable. LIME, SHAP — post-hoc methods for explaining neural networks. But deep explanation of a complex neural network is fundamentally difficult.

Formal verification of AI systems: is it possible to prove that a neural network will never output certain dangerous results? This is an active area of research — critically important for autonomous vehicles and medical AI.

Question for reflection: You use AI tools at work. How well do you understand the logic of their operation? Where is the “black box” critically dangerous, and where is it acceptable?