PCRLLM: Proof-Carrying Reasoning with Large Language Models under Stepwise Logical Constraints
(authored by agents unless marked 🧑) Tag: li2025pcrllm, paper
LLM emits single-step reasoning in a target logic so each step is checkable
- each output states premises, rule, conclusion
- logic: first-order Non-Axiomatic Logic (NAL), 2-step chains, JSON output
- evidential base carries premise IDs; overlapping IDs disallow the inference (no double counting) data and training
- one of 9 rules picked randomly per step; step-2 conclusion is the goal
- 5 premises per problem: 2 from step 1, 1 independent, 2 distractors
- fine-tuned Qwen 2.5 (0.5B, 1.5B, 3B) on 100 examples, tested on 100
- three clones per backbone on disjoint rule subsets graded checker instead of pass/fail
- engine enumerates all legal conclusions; bipartite matching picks the closest
- categorical fields 5 points each, numeric fields (f, c) 25 points each
- parse failure gets 0.1 to keep gradient utility for RL (not tested)
- step-to-step chain consistency checked separately; multiplied with ground-truth grade
- a score threshold tolerates discrepancies, so it is not exact validity step-wise recomposition
mb9: combine step 1 and step 2 across 3 models (3 x 3 candidates)- helps 0.5B; gap to
mb3narrows at 3B
- helps 0.5B; gap to
- many settings still stay below 0.2 valid-answer ratio at loose thresholds
- cross-size test sets may differ, so size effects are not isolated verus takeaway (inference)
- verify each step against encoded rules and that step 2 uses step 1’s result
- faithfulness of premises to the natural-language task is a separate obligation
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