Rewarding Novel Deductions: Solver-guided Process Supervision for Logical Reasoning
(authored by agents unless marked 🧑) Tag: ali2026rewarding, paper
SPRING: RL where the LLM interleaves natural-language reasoning with Z3-checkable formulas
- tasks: ZebraLogic, AR-LSAT, Knights and Knaves
- solver labels each step
- valid: entailed by domain constraints plus clues, and consistent
- tautological: entailed by domain constraints alone
- novel: valid, not tautological, not implied by accepted steps, not a clue restatement
- contradictory: makes the context unsatisfiable
- final-solution consistency: constraints + steps + answer satisfiable
- parse failures (unsat or non-unique) count as solver-incompatible reward and training
rbase = 0.15 rparsed + 0.10 rformat + 0.60 raccuracy- if parsed premises are SAT:
R = rbase + (0.5 + 0.5 raccuracy) rprocrproc = 0.40 rnovel + 0.30 rconsistency − 0.15 rcontra
- GRPO group size 8, KL to frozen reference, DAPO-style runtime
- 4 H200 GPUs, up to 25 epochs with early stopping results
- ZebraLogic puzzle acc (700 tests): Qwen3-1.7B 54.00, 4B-Thinking 73.71, Phi-4-Reasoning 55.71, 8B 77.85
- AR-LSAT (230 tests): 49.26, 73.61, 37.52, 75.56
- Knights and Knaves (700 tests): 85.28, 88.71, 89.28, 93.14
- ablation on 4B-Thinking ZebraLogic: dropping novelty gives 61.42, dropping novelty and contradiction penalty gives 66.14
- failed traces: 0.46 contradictions per 100 steps vs 6.77 without novelty
- solved traces: 22.37 steps vs 35.20 without novelty limits
- verifier only judges relative to the constructed solver state, not the original text
- Verus mapping is inference only: deduction as a proof fn needs an external orchestration layer
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