VeriLogic: Reinforcement Learning over Verifiable Logical Reasoning Traces

Logical reasoning derives conclusions from premises through explicit intermediate inference steps, providing a natural basis for process-level verification and supervision. However, existing learning methods often rely on response-level outcome signals, which overlook heterogeneous correctness within the reasoning trace: a correct answer may contain invalid reasoning, while valid intermediate steps may also appear in an incorrect response. To address this issue, we introduce Reinforcement Learning on Verifiable Logical Reasoning (VeriLogic), which turns internal reasoning traces into explicit and verifiable learning objects. Rather than treating a response as an indivisible learning unit, VeriLogic decomposes logical reasoning into explicit intermediate judgments, proofs, and final decisions, and organizes them into a unified “Grounding - Optimization - Refinement” pipeline: (1) Verification-Grounded Reasoning Environment Construction grounds logical reasoning into explicit intermediate states and formally checkable proof obligations, making the internal reasoning process accessible to verification and learning; (2) Logical Structured Policy Optimization learns from verifier feedback through complementary global and local rewards, jointly optimizing the overall reasoning outcome while providing targeted optimization signals to different intermediate reasoning paths; and (3) Verifier-Guided Iterative Refinement acts on verifier feedback by leveraging proof states and error messages to iteratively diagnose and repair failed reasoning. Experiments on six logical reasoning benchmarks show consistent gains over strong baselines, with average improvements of 6.39% and 5.00% on Qwen3 and Llama-3.1. These results highlight the value of making logical reasoning traces verifiable, learnable, and refinable beyond final-answer supervision.