Constructive Symbolic Reinforcement Learning via Intuitionistic Logic and Goal-Chaining Inference
This work addresses the need for safe and interpretable planning in AI, particularly for applications requiring guaranteed logical validity, though it is incremental as it builds on existing symbolic and logical methods.
The paper tackles the problem of unsafe or invalid transitions in reinforcement learning by introducing a constructive logical inference framework that replaces reward-based optimization with intuitionistic logic and goal-chaining, achieving perfect safety and efficient convergence with no invalid actions in a gridworld environment.
We introduce a novel learning and planning framework that replaces traditional reward-based optimisation with constructive logical inference. In our model, actions, transitions, and goals are represented as logical propositions, and decision-making proceeds by building constructive proofs under intuitionistic logic. This method ensures that state transitions and policies are accepted only when supported by verifiable preconditions -- eschewing probabilistic trial-and-error in favour of guaranteed logical validity. We implement a symbolic agent operating in a structured gridworld, where reaching a goal requires satisfying a chain of intermediate subgoals (e.g., collecting keys to open doors), each governed by logical constraints. Unlike conventional reinforcement learning agents, which require extensive exploration and suffer from unsafe or invalid transitions, our constructive agent builds a provably correct plan through goal chaining, condition tracking, and knowledge accumulation. Empirical comparison with Q-learning demonstrates that our method achieves perfect safety, interpretable behaviour, and efficient convergence with no invalid actions, highlighting its potential for safe planning, symbolic cognition, and trustworthy AI. This work presents a new direction for reinforcement learning grounded not in numeric optimisation, but in constructive logic and proof theory.