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CEDAR-GRPO: Process-Aware Reinforcement Learning for General Abductive Reasoning in LLMs

Moein Salimi, Danial Parnian, Shaygan Adim, Amirmohammad Ebrahiminasab, Nima Alighardashi, Parsa Gholami, Sahand Akramipour, Mahdi Jafari Siavoshani, Mohammad Hossein Rohban

arXiv:2608.14791v1cs.AI

TL;DR

LLM abduction has mainly been studied on narrow, task-specific benchmarks, leaving transfer beyond training or evaluation benchmark families unclear. CEDAR-GRPO combines correctness with evidence-coverage and directionality rewards, improving every model on every held-out task over base models and correctness-only GRPO.

  • Problem

    LLM abduction research has relied mainly on narrow benchmarks, leaving transfer across domains, task formats, and verification regimes unclear.

  • Method

    CEDAR-GRPO post-trains models with final-answer correctness plus rewards for evidence coverage and observation-to-explanation directionality across heterogeneous hypothesis-generation and selection tasks.

  • Results

    CEDAR-GRPO improved every model on every held-out task over base models and correctness-only GRPO, averaging 7.4 points over base models and 2.7 over Cor-GRPO.

  • Takeaways & Limitations

    The results support abductive reasoning as a transferable capability strengthened across four backbones and 11 held-out tasks.

  • Takeaways & Limitations

    Evaluation remains largely benchmark-style with closed-form outcomes, leaving generalization to open-ended or interactive explanatory tasks unclear.

Abstract

from arXiv · show

Abductive reasoning, often characterized as inference to the best explanation, is central to explanation under uncertainty, from everyday sense-making and investigation to scientific discovery. Yet LLM research has mostly studied abduction through narrow, task-specific benchmarks, making it unclear whether observed gains transfer beyond the benchmark family used for training or evaluation. We ask whether RL post-training can improve abduction as a transferable reasoning capability. We introduce CEDAR-GRPO, a process-aware framework that combines final-answer correctness with abductive rewards for evidence coverage and evidence-to-explanation directionality. Four open-weight LLMs are post-trained on a controlled, domain-neutral mixture of abductive hypothesis-generation and hypothesis-selection tasks. We evaluate them on 11 unseen tasks spanning hypothesis selection, missing-fact generation, defeasible inference, long-context investigation, clinical reasoning, code debugging, and non-abductive controls. CEDAR- GRPO improves every model on every held-out task over both base models and correctness-only GRPO, with average gains of 7.4 and 2.7 points, respectively, and a maximum gain of 30.8 points. Ablations confirm that RL, abductive reward design, and task diversity each contribute to transfer. Process-level metrics further show stronger abductive behavior, including exploration of alternatives, elimination of rivals, backtracking, and uncertainty marking.

1 Introduction

The paper frames abduction as inferring hidden explanations from incomplete evidence and asks whether reinforcement-learning post-training can improve it as a transferable capability. It introduces CEDAR-GRPO, evaluates transfer across four open-weight backbones and 11 unseen tasks, and reports consistent gains over base models and correctness-only GRPO.

  • Motivation: Abductive reasoning infers a hypothesis from observations that would make them less surprising, supporting diagnosis, scientific hypothesis formation, debugging, and long-context investigation.The paper describes this as inference to the best explanation and motivates it through clinical, engineering, and investigative scenarios.
  • Motivation: Existing evaluations often remain within one benchmark family, task format, or structured domain, obscuring whether methods learn reusable abduction or narrow adaptations.The paper distinguishes hypothesis generation from hypothesis selection as two principal abductive task forms.
  • Method: CEDAR-GRPO combines deterministic final-answer correctness with rewards for observed-evidence coverage and observation-to-explanation directionality.Correctness uses exact-match, label-based, or execution-based verification, while the abductive rewards are process-aware.
  • Experimental design: Four open-weight backbones are post-trained on a controlled, domain-neutral mixture spanning hypothesis generation, hypothesis selection, missing-fact generation, and rule learning, then evaluated on 11 unseen tasks.The evaluation includes direct abductive targets, abduction-adjacent transfer tasks, and non-abductive controls across reasoning domains.

2 Related Work

Prior abduction research spans diverse explanation, missing-fact, causal, clinical, and hypothesis-generation tasks, but improvements often remain entangled with task-specific domains and evaluation formats. Existing methods have mainly used supervised adaptation or inference-time scaffolding, leaving broad transfer from reinforcement-learning post-training unresolved.

  • Abductive reasoning benchmarks: Abductive NLP benchmarks cover commonsense hypothesis selection, causal reasoning, clinical diagnosis, missing-fact generation, and structured hypothesis generation.Examples include ART, UNcommonsense, e-CARE, DDXPlus, ProofWriter, AbductionRules, and structured generation over k.
  • Transfer limitations: Existing benchmarks can confound abductive improvements with particular domains, output formats, or verification regimes.This motivates evaluating abduction as a broader capability across hypothesis-generation and hypothesis-selection settings beyond training tasks.
  • Prior improvement methods: Prior approaches have largely relied on supervised adaptation, ranking or preference objectives, prompting, retrieval, multi-agent decomposition, and symbolic checking.These methods improve task-specific adaptation or inference control but do not establish broadly generalizable abductive behavior.
  • Reinforcement learning for abduction: Reinforcement learning has been used narrowly for abduction, including PPO-style knowledge-graph feedback and GRPO-based reinforcement pipelines.CEDAR-GRPO differs by targeting broad abductive transfer with verifiable correctness plus process-aware rewards for evidence coverage and evidence–explanation directionality.
  • Process-aware reinforcement learning: CEDAR-GRPO draws on process-supervision research while avoiding reliance on human-labeled reasoning traces.Its process-aware reward design focuses on evidence coverage and evidence–explanation directionality.

3 Data Collection

The data collection separates abduction into hypothesis generation and hypothesis selection, using a broad, non-specialized training pool and a broader evaluation suite. Evaluation spans classic abductive benchmarks, neighboring domains, and non-abductive controls to test transferable reasoning without conflating generation and selection.

  • Data Collection: Abductive reasoning is divided into Stage I hypothesis generation and Stage II hypothesis selection, allowing improvements in proposing hypotheses, evaluating candidates, or both to be distinguished.This separation avoids conflating distinct sources of improvement.
  • Data Collection: The training pool uses broadly non-specialized resources spanning both abductive stages, combining selection tasks with generation tasks that construct missing hypotheses.Selection tasks provide plausibility-judgment signals, while generation tasks avoid restricting learning to closed-set answer selection.
  • Data Collection: The evaluation suite is broader than training, including ART (αNLI), NeuLR’s abductive split, and Defeasible NLI across hypothesis selection, missing-fact generation, and evidence-sensitive judgment.These datasets cover classic abductive benchmarks and a Stage II-adjacent evidence-strength assessment.
  • Data Collection: Transfer evaluation covers latent affect inference, culprit inference, clinical diagnosis, and software diagnosis and repair, alongside forward-causal, long-context, and general-reasoning controls.The neighboring-domain tasks are GoEmotions, MuSR: Murder, MedQA, and ML-debugging; controls include Balanced COPA, MuSR: Object, MuSR: Team, and StrategyQA.

4 Methodology

CEDAR-GRPO operationalizes abduction as selecting or generating explanations for incomplete observations and trains four open-weight backbones on structured reasoning outputs. Its process-aware objective combines answer correctness with evidence coverage and evidence-to-explanation directionality, optimized using GRPO.

  • Abduction and Models: Abductive reasoning is defined as selecting or generating the explanation that best accounts for incomplete observations, including causes, missing facts, and transformation rules.The experiments use Qwen3-4B, Qwen3-8B, DeepSeek-R1-Distill-Qwen-7B, and Llama-3.1-8B-Instruct, spanning 4B–8B parameters.
  • Structured Outputs: Models produce structured outputs separating a reasoning trace β from a final answer α; correctness is computed from α, while process rewards use the prompt and β.The output format is ⟨think⟩β ⟨/think⟩⟨answer⟩α ⟨/answer⟩.
  • Process Rewards: Coverage rewards whether observation details are addressed, with the judge returning m details and marking each as addressed or unaddressed.If no valid detail list is returned, the coverage reward is zero.
  • Process Rewards: Directionality rewards traces at 0, 0.5, or 1 according to whether reasoning assumes an explanation, is mixed, or proceeds from evidence toward an explanation.Both process rewards are scored from the prompt and reasoning span, whereas correctness is computed only from the final answer.
  • Optimization: For each prompt, the method samples G = 4 completions and optimizes with Group Relative Policy Optimization without a separate value network.All backbones use NF4 quantization and LoRA fine-tuning.

5 Experiments

Experiments evaluate CEDAR-GRPO’s transfer beyond training formats through held-out task performance, process-level reasoning metrics, and ablations of RL, reward design, training stages, and task composition. CEDAR-GRPO improves abductive performance and induces stronger evidence-grounded, exploratory reasoning than correctness-only and restricted alternatives.

  • Held-out task performance: The evaluation compares base models, correctness-only Cor-GRPO, and composite-reward CEDAR-GRPO across held-out abductive, abduction-adjacent, and non-abductive tasks.The suite tests transfer beyond the training formats and separates gains from RL itself from gains due to the composite reward.
  • Held-out task performance: CEDAR-GRPO consistently improves over Cor-GRPO on the held-out suite, indicating that coverage and directionality rewards contribute beyond correctness optimization.The comparison is designed to distinguish gains from RL itself from gains attributable to the composite process reward.
  • Process-level evaluation: Evidence Coverage increases from 33.1% to 52.9%, while Evidence–Explanation Directionality rises from 0.21 to 0.60 under CEDAR-GRPO.Cor-GRPO’s Directionality drops to 0.16, showing that correct answers can occur without a sound evidence-to-conclusion flow.
  • Process-level evaluation: CEDAR-GRPO raises Differential Elimination from 0.79 to 1.29 and Backtracking from 0.69 to 1.09, while increasing Branchiness to 1.53 and Prior Invocation to 0.72.These changes reflect greater exploration of alternatives, candidate explanations, and distinct reasoning paths.
  • Reward ablations: On Qwen3-4B, CEDAR-GRPO reaches 52.1 average accuracy versus 50.3 for Cor+Cov-GRPO and 50.2 for Cor+Dir-GRPO; on DeepSeek-R1-Distill-Qwen-7B, scores are 54.1, 51.1, and 50.7.The full composite reward outperforms either partial process objective, supporting complementarity between coverage and directionality.
  • Training-mixture ablations: On Qwen3-4B, CEDAR-GRPO reaches 52.1 average accuracy versus 49.3 for Stage I-only and 48.4 for Stage II-only; on DeepSeek-R1-Distill-Qwen-7B, scores are 54.1, 49.6, and 49.9.The full mixture’s advantage indicates that generation- and selection-oriented data provide complementary transfer signals.

6 Conclusion

CEDAR-GRPO frames abduction as a general reasoning capability rather than a benchmark-specific skill. Across four open-weight backbones and eleven held-out datasets, it consistently outperformed both base models and correctness-only GRPO, with gains up to 30.8 points and transfer to adjacent settings.

  • CEDAR-GRPO is introduced as a composite-reward post-training framework for treating abduction as a general reasoning capability.
  • Across four open-weight backbones and eleven held-out datasets, CEDAR-GRPO consistently improved performance over both base models and correctness-only GRPO.
  • 30.8 points was the maximum gain, with transfer to clinical diagnosis, ML debugging, and long-context investigation.

7 Limitations · A Additional Dataset Notes for Data Collection

The paper identifies limitations in evaluation openness, model scale, and the reliance on LLM-based judgments for both training rewards and process-level assessment. It also documents dataset-operationalization choices that may differ from the original benchmark definitions, including narrower subsets.

  • 7 Limitations: Evaluation remains constrained by benchmark-style settings and largely closed-form outcomes.The paper notes that extension to truly open-ended or interactive explanatory tasks remains unclear.
  • 7 Limitations: The gains’ applicability to open-ended or interactive explanatory tasks with non-predefined answer spaces remains unclear.
  • 7 Limitations: All evaluated backbones fall within the 4–8B parameter range.
  • 7 Limitations: Process-level metrics are computed by an LLM-as-judge, introducing a potential evaluation concern.The authors state that these metrics are intended to validate changes in reasoning behavior.
  • 7 Limitations: Shared LLM-based judgments create potential circularity between optimization signals and evaluation.Evidence-coverage and directionality rewards used during training rely on the same kind of judgments as the evaluation metrics.
  • 7 Limitations: Human evaluation would strengthen conclusions about reasoning quality.The proposed checks cover process-level scores on the existing evaluation suite and dedicated human evaluation.
  • A Additional Dataset Notes for Data Collection: The dataset notes distinguish each original benchmark from how it is operationalized in this study.This matters because some datasets are released as task collections or reasoning-type subsets rather than fixed train/dev/test corpora.
  • A Additional Dataset Notes for Data Collection: Several study subset choices are narrower than the corresponding benchmarks as a whole.

A.1 Training and validation sources

Training and validation use a balanced, domain-neutral mixture of abductive, causal, verification, rule-learning, and latent-transformation datasets. The full pool contains 2,400 samples split into 1,920 training and 480 validation examples.

  • Additional training sources: Additional sources cover balanced cause selection, climate claim–evidence relations, latent list transformations, and Caesar–Atbash cipher rule induction.List Function treats the hidden transformation as a missing explanatory rule, while Crypto is used as Stage I rule-learning data.
  • Abductive and causal sources: CauseLogics contributes 320 training and 80 validation examples balanced across four reasoning-chain difficulty levels.The benchmark uses premises, rules, a phenomenon, a candidate cause, and a binary validity label.
  • Abductive and causal sources: AbductionRules supplies balanced formal abduction data across four variants, where models infer missing facts that explain unexpected observations.The variants are Abduction-Animal-Simple, Abduction-Animal, Abduction-Person-Simple, and Abduction-Person.
  • Dataset composition: The dataset pool totals 2,400 samples, divided into 1,920 training and 480 validation examples, with 400 samples for most datasets and 200 for Crypto and List Function.Each dataset follows an 80/20 train/validation split.

A.2 Evaluation sources · B Prompts Used in Training and Evaluation · C Training and Implementation Details

The paper evaluates abductive transfer across classic, domain-shifted, and non-abductive benchmarks, while using structured prompts that enforce task-specific reasoning and exact answer formats.

  • A.2 Evaluation sources: ART tests two-choice hypothesis selection between observations, whereas NeuLR uses 400 abductive examples for content-neutral missing-fact generation.ART is used for Stage II selection and NeuLR for Stage I generation.
  • A.2 Evaluation sources: Defeasible NLI evaluates whether an update strengthens or weakens a hypothesis, while GoEmotions, MuSR-M, MedQA, and ML-debugging extend abduction into neighboring domains.MuSR-M emphasizes explanatory sequences in long narratives; MedQA infers clinical problems, and ML-debugging traces failures to causes before repair.
  • A.2 Evaluation sources: MuSR-O/T, Balanced COPA-effect, and StrategyQA serve as non-abductive controls involving assignments, forward causal effects, or implicit multistep reasoning.These controls separate backward explanatory reasoning from other long-context and general-reasoning capabilities.
  • A.2 Evaluation sources: The held-out suite spans classic abduction, evidence updates, neighboring-domain abduction, and explicit non-abductive controls.This design creates an intentional gradient for interpreting whether gains are directly abductive or reflect broader reasoning.
  • B.1.1 Prompt Template: UniADILR: Training prompts for UniADILR require selecting context sentences that logically support a hypothesis, with step-by-step reasoning and comma-separated sentence-number answers.The answer section is constrained to sentence numbers only.
  • B.1.4 Prompt Template: Climate Fever / B.1.5 Prompt Template: Abduction Rules: Climate Fever classifies evidence as SUPPORTS, REFUTES, DISPUTED, or NOT ENOUGH INFO, while Abduction Rules generates one missing fact that makes a query decidable.The Abduction Rules prompt requires a direct, minimal fact and permits proving either the query or its opposite.
  • B.2 Prompt Templates / B.1.6 Prompt Template: Crypto System Prompt: / B.1.7 Prompt Template: List Function: Evaluation prompts preserve task-specific reasoning: ART bridges observations, Copa-effect predicts consequences, DefensibleNLI assesses updates, GoEmotion labels emotions, MedQA selects diagnoses, and MuSR solves indexed choices.Crypto and List Function prompts additionally infer transformations from examples and return exactly one generalized Python function.

C.1 Hyperparameters and Model Specifications · C.2 Compute and Reproducibility

The implementation uses memory-efficient, parameter-efficient post-training across four open-weight models with a shared quantized LoRA setup. Training and evaluation run on a single GPU with fixed random seeds, while reward judging is performed remotely.

  • C.1 Hyperparameters and Model Specifications: Unsloth supports memory-efficient post-training for DeepSeek-R1-Distill-Qwen-7B, Qwen3-4B, Qwen3-8B, and Llama-3.1-8B-Instruct.The pipeline covers four model architectures.
  • C.1 Hyperparameters and Model Specifications: All four models use 4-bit NormalFloat (NF4) quantization.The quantization choice is shared across model architectures.
  • C.1 Hyperparameters and Model Specifications: All four models use Low-Rank Adaptation (LoRA) for post-training.LoRA is part of the shared configuration reported in Table 7.
  • C.2 Compute and Reproducibility: Training and evaluation were conducted locally on one NVIDIA GeForce RTX 5090 GPU with 32 GB GDDR7.The pipeline used no multi-GPU parallelism.
  • C.2 Compute and Reproducibility: The gpt-oss-120b reward judge was accessed remotely.Reward judging was separate from the local single-GPU training and evaluation setup.
  • C.2 Compute and Reproducibility: The pipeline-level random state is fixed to 3407, while PyTorch and NumPy seeds are fixed to 42.These settings define the reported reproducibility configuration.

D Reward Function Formulation · E Process-Level Metrics

CEDAR-GRPO combines correctness with Evidence Coverage and Evidence–Explanation Directionality rewards, computed from extracted reasoning and answer spans by online judges. The process metrics are selected for broad applicability and lower reward-hacking risk, while dataset-specific notes define how evidence and candidate explanations are identified.

  • D.1 Composite Objective: The GRPO reward is computed from prompt, completion, ground truth, and dataset inputs, with reasoning and answer text extracted from <think> and <answer> spans.Cor-GRPO applies no additional transformation and uses only rcor.
  • D.2 Correctness Reward: Correctness verification assigns rcor = 0 when the <answer> span is absent and executes code tests in separate processes with five-second timeouts.For executable tasks, optional Markdown fences are removed before testing.
  • D.3 Process Rewards: Evidence Coverage scores whether the reasoning trace explicitly connects each judge-extracted observation detail to the chosen hypothesis.The denominator is the number of details returned by the judge, with no alias merging or deduplication.
  • D.3 Process Rewards: The directionality judge distinguishes explanation-to-evidence, mixed, and evidence-to-explanation reasoning, assigning zero to invalid or unparseable outputs.If the <think> span is absent, the full completion is passed to process judges; both use openai/gpt-oss-120b at temperature 0.0 across all seven training datasets.
  • D.4.1 Evidence Coverage System message: Training-time coverage judges exhaustively extract main and peripheral details, then mark each addressed only when the trace directly explains its connection to the hypothesis.These prompts are distinct from generator prompts and post-hoc evaluation prompts.
  • D.4.2 Evidence–Explanation Directionality: Directionality prompts enforce forward reasoning from known observations toward the best hypothesis, scoring proper, mixed, and reverse reasoning as 1.0, 0.5, and 0.0.Assuming an explanation and checking whether it predicts the observations is treated as a logical flaw for this metric.
  • D.4.3 Dataset-Specific Notes: Dataset-specific notes map observations and candidate explanations differently across UniADILR, BalancedCOPA, CauseLogics, ClimateFever, AbductionRules, ListFunction, and Crypto.The notes specify the evidence fields and the expected direction of reasoning for each training dataset.
  • D.5 Reward Metric Selection: Evidence Coverage and Evidence–Explanation Directionality were selected as primary process rewards because they support required reasoning behavior while presenting lower reward-hacking risk than Backtracking or Uncertainty Markers.Coverage applies across selection, verification, and generation settings, while directionality preserves abductive flow from evidence toward explanation.

E.1 Evaluation Framework … E.4 Judge Prompts

The evaluation uses deterministic, zero-shot Gemini 3 Flash judging with metric-specific prompts and dataset-specific framing. Seven process-level metrics quantify uncertainty, alternative exploration, correction, elimination, priors, evidence coverage, and evidence-to-explanation directionality.

  • E.1 Evaluation Framework: All seven process-level metrics use Gemini 3 Flash with metric-specific structured prompts, deterministic JSON parsing, dataset framing, and no few-shot demonstrations.The judge receives each reasoning trace and returns a fixed JSON schema; evaluations are strictly zero-shot.
  • E.2 Metric Definitions: The framework combines five counting metrics with Evidence Coverage and score-based Evidence–Explanation Directionality, reporting per-trace counts or averaged discrete scores.Counting metrics extract concrete occurrence pairs; directionality assigns 0.0, 0.5, or 1.0, averaged over the dataset.
  • E.2.1 Uncertainty Markers; E.2.2 Branchiness: Uncertainty Markers count individual epistemic hedges, while Branchiness counts substantively distinct candidate explanations and excludes mere rephrasings or linear procedural narration.Their reported statistics are mean marker occurrences and mean branching instances per trace, averaged over the dataset.
  • E.2.3 Backtracking; E.2.4 Differential Elimination: Backtracking counts explicit error-driven revisions, whereas Differential Elimination counts evidence-grounded refutations of alternatives and excludes unsupported dismissals or positive support alone.Both metrics require distinct reasoning events rather than final answer selection or merely contrasting valid paths.
  • E.2.5 Prior Invocation: Prior Invocation counts explicit base rates, typicality, comparative likelihoods, or Bayesian prior reasoning, excluding posterior-only conclusions and general facts without frequency content.The metric reports mean priorinvocation instances per trace, averaged over the dataset.
  • E.2.6 Evidence Coverage: Evidence Coverage atomizes every observation detail and marks it addressed only when the trace makes a clear logical connection to the chosen hypothesis.The reported mean scov is expressed as a percentage in tables.
  • E.2.7 Evidence–Explanation Directionality: Evidence–Explanation Directionality scores whether reasoning proceeds from fixed observations toward an explanation rather than assuming a hypothesis and verifying its predictions.The judge assigns 1.0 for clear evidence → explanation reasoning, 0.5 for ambiguous or mixed directionality, and 0.0 for backward or deductive direction.
  • E.3 Dataset-Specific Judge Notes; E.4 Judge Prompts: Judge prompts provide dataset-specific metric definitions and verbatim system and user templates, replacing {dataset_specific_note} at runtime while requiring valid JSON outputs.The supplied prompts operationalize extraction and exclusion rules for the process metrics, including uncertainty markers, branching, correction, elimination, priors, and coverage.

E.5 Detailed Per-Dataset Results

This section reports DeepSeek-R1-Distill-Qwen-7B’s dataset-specific process-level scores and explains how the metrics and judge-prompt notes are defined. Table 10 compares three conditions within each metric–dataset cell.

  • Per-dataset process-level scores: Table 10 reports per-dataset process-level metric scores for DeepSeek-R1-Distill-Qwen-7B across three conditions.Bold values indicate the maximum for each metric–dataset cell.
  • Metric definitions: Counting metrics are reported as mean occurrence counts per trace, while Evidence Coverage and Directionality are reported as mean scores.These reporting conventions apply to the values in Table 10.
  • Dataset-specific judge notes: Dataset-specific notes provide the exact text appended to the shared system prompt for every process-level metric.The notes are presented across Table 11 and its continuation.

F SFT Data Construction and Training Details … G.1 Mixture composition

The SFT ablation uses validated synthetic rationales in the same response format and data split as GRPO, then trains Qwen3-4B and DeepSeek-R1-Distill-Qwen-7B baselines with masked assistant-token cross-entropy. Dataset-specific prompts constrain rationales to evidence- or rule-grounded explanations while preserving exact gold answers, and a balanced six-benchmark auxiliary mixture tests general-reasoning transfer.

  • F SFT Data Construction and Training Details: SFT examples reuse GRPO training sources, inserting synthetic rationales into <think> blocks while retaining the original gold answer.The resulting target uses the same <think>–<answer> structure as GRPO policy outputs.
  • F SFT Data Construction and Training Details: Synthetic rationales are accepted only after exact format and gold-answer validation, with generated code additionally compiled and executed for code-generation datasets.Classification and selection answers must exactly match normalized labels or sentence-number sets, while AbductionRules must match the gold missing fact.
  • F SFT Data Construction and Training Details: 1,920 training and 480 validation examples form the mixed SFT dataset, with the same GRPO split and dataset-specific contributions.The mixed split is shuffled with seed 42 after each sample is tagged by dataset name.
  • F.2 Synthetic-rationale prompt templates: The rationale-generation templates require concise, formatted explanations grounded in the supplied task inputs and gold answers, while keeping answer blocks unchanged.Templates cover evidence selection, causal comparison, logical rule chains, claim evaluation, missing facts, and code rule induction.
  • F.2 Synthetic-rationale prompt templates: Crypto and List Function targets require Python implementations whose held-out tests pass before the accompanying rationale is accepted.Crypto uses at most the first ten normal training examples in rationale generation; List Function requires a single transform(lst) function.
  • G Additional Dataset Notes for the General-Reasoning Ablation: The general-reasoning ablation uses a balanced auxiliary mixture of GSM8K, FOLIO, CommonsenseQA, VitaminC, MMLU, and BIG-Bench.Its purpose is to test whether improvements attributed to abductive training persist beyond a single benchmark family.

G.2 Dataset-specific notes · G.3 Interpretation

G.2 describes a balanced, heterogeneous general-reasoning ablation mixture spanning quantitative, formal-logical, commonsense, evidence-conditioned, academic, and broad reasoning tasks. G.3 interprets it as a controlled training condition for testing whether improvements are specific to abductive supervision rather than a general reasoning curriculum.

  • G.2 Dataset-specific notes: GSM8K contributes multi-step grade-school mathematics problems, using 320 training and 80 validation instances to assess reliable numeric answer derivation.The ablation targets final numeric answers rather than the benchmark’s worked solutions.
  • G.2 Dataset-specific notes: FOLIO contributes 320 training and 80 validation examples for determining whether conclusions follow from first-order-logic premises.Its uncertainty class probes preservation of calibrated three-way logical judgments under mixed-task training.
  • G.2 Dataset-specific notes: The mixture contains 2,400 examples, with 400 instances from each source and an 80/20 train/validation split.Equal allocation prevents domination by any single benchmark family and supports comparison against abductive training.
  • G.2 Dataset-specific notes: CommonsenseQA supplies 320 training and 80 validation questions as broad commonsense supervision, counterbalancing formal and domain-specific benchmarks.It is a five-way multiple-choice benchmark requiring everyday background knowledge rather than shallow textual matching.
  • G.2 Dataset-specific notes: VitaminC contributes contrastive fact-verification instances whose wording, numbers, or negation edits can change labels, while preserving approximate class proportions.Its training split contains 160 SUPPORTS, 114 REFUTES, and 46 NOT ENOUGH INFO examples.
  • G.2 Dataset-specific notes: MMLU contributes 320 training and 80 validation questions across eight academic subjects, while BIG-Bench adds four reasoning-oriented tasks with 100 examples each.BIG-Bench broadens task diversity beyond standard question answering through logical deduction, object tracking, date understanding, and table reasoning.
  • G.3 Interpretation: The corpus is a controlled training mixture for ablation analysis, not a benchmark, testing whether gains arise specifically from abductive supervision or from a similarly sized general curriculum.Its heterogeneity covers quantitative reasoning, formal validity, everyday inference, evidence-conditioned judgment, and broader subject and task diversity.
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