From Black Box to Executable Logic: Explainable Reinforcement Learning through Prolog Expert Systems
This paper proposes a method to convert deep reinforcement learning policies into executable Prolog logic programs for explainability. It uses a three-stage post-hoc transformation: extracting a frozen PPO teacher, inducing an ordered rule list, and emitting a Prolog program, followed by an expansion stage that certifies return improvements. Theoretical guarantees include return-loss bounds, monotonic improvement, and fidelity control in continuous domains. Empirically, it achieves exact optimal returns on a discrete task and matches or approaches neural teacher performance on continuous control tasks.
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[Submitted on 16 Jul 2026]
Title:From Black Box to Executable Logic: Explainable Reinforcement Learning through Prolog Expert Systems
View a PDF of the paper titled From Black Box to Executable Logic: Explainable Reinforcement Learning through Prolog Expert Systems, by Eduardo C. Garrido-Merch\'an
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Abstract:A trained deep reinforcement learning policy is a black box, and we ask whether it can be made explainable by rewriting it as an executable logic program that reproduces its behaviour and that a person can read, a logic engine can run, and an optimizer can edit. We present a three-stage post-hoc transformation that extracts a frozen proximal policy optimization teacher, induces an ordered rule list from its decisions in the manner of classical relational learning, and emits the result as a Prolog program whose every decision is executed by an off-the-shelf logic engine; a subsequent expansion stage edits the rule base and accepts an edit only when policy evaluation certifies a return increase. We prove four guarantees. A return-loss bound makes the distilled program a machine-checkable certificate in a finite Markov decision process, and the expansion loop improves monotonically and terminates. For the continuous-observation setting we answer whether the conversion is possible at all: the propositional threshold instantiation converts the network to arbitrary fidelity as the resolution B grows, with disagreement O(1/B) and a return gap that closes at the same rate, and a matching lower bound shows the cost is exponential in the observation dimension for an oblique decision boundary. Empirically, on a two-room key-and-door task with 16,944 reachable states the expanded Prolog program attains exact optimal return in every seed and, in a budget-capped regime, exceeds the stochastic teacher on exact return in ten of ten seeds. On three continuous-control tasks the emitted program substitutes the network, matching the neural teacher within noise on Acrobot with eleven clauses and recovering about 97% of its return on CartPole, while on the finer-control LunarLander it recovers only partially, exactly the ceiling the exponential lower bound predicts.
Subjects:
Artificial Intelligence (cs.AI)
Cite as: arXiv:2607.15459 [cs.AI]
(or arXiv:2607.15459v1 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2607.15459
arXiv-issued DOI via DataCite (pending registration)
Submission history
From: Eduardo C. Garrido-Merchán [view email] [v1] Thu, 16 Jul 2026 21:10:27 UTC (49 KB)
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