Recent progress in large language model reasoning has been driven by benchmarks and reinforcement learning environments with automatically verifiable rewards, particularly in mathematics, code, and formal logic. These settings make model accuracy easier to evaluate and optimize, but it remains unclear how far success under fixed problem specifications and stable evaluation criteria transfers to reasoning outside such domains. Real-world reasoning often proceeds under incomplete and revisable information: conclusions may be supported provisionally, defeated by counter-evidence, reinstated by further arguments, or revised when stronger reasons become available. Reasoning of this kind is generally referred to as defeasible reasoning. We introduce ArgGYM, a procedural benchmark and RLVR-compatible training environment for structured defeasible reasoning. ArgGYM decomposes this reasoning into twelve tasks and grounds task-specific scoring in a symbolic argumentation engine that computes the formal states used to evaluate model outputs. It includes a frozen benchmark of 1,440 verified instances across fifteen curriculum configurations, two argument preference orderings (weakest-link and last-link), and two set orderings (elitist and democratic), while the same generators and verifiers can produce fresh instances for evaluation that reduces dependence on static test sets and for verifiable-reward training. On the frozen benchmark, frontier and open-weight models show sharply different reasoning profiles: they can recover substantial parts of structured answers without solving the complete task, and performance declines in later curriculum configurations with longer dependencies and more interacting structures. We release the benchmark, generators, and verifiers for reproducible evaluation and RLVR training.
Figures & tables
Task
Objective
Representation and support
formalization
Construct an executable ASPIC+ theory from a controlled natural-language description whose induced argumentative state is behaviorally equivalent to the intended theory.
claim_chain
Recover the complete support derivation for a justified target claim in an ordering consistent with its derivational dependencies.
Diagnosis, semantics, and revision
defeat_diagnosis
Identify where support for a non-justified target fails and the relevant defeaters responsible for that failure.
status_query
Determine the statuses of queried claims under grounded semantics.
Table 1: The twelve ArgGYM tasks. The first six require structured analysis or formalization outputs, while the final six require constructive interventions whose consequences are executed and verified through the task-specific scoring pipeline.
Table 3: Model and inference configurations. T denotes temperature, p top- p , k top- k , and PP presence penalty. Max. out. is the maximum generated-token budget.
Model
Reasoning
Formal.
Chain
Diagnosis
Status
Semantics
Perturb.
Gemma
google/gemma-4-E2B-it
off
0.8 ∣ 1.0
2.5 ∣ 3.5
5.0 ∣ 13.1
1.7 ∣ 47.6
0.0 ∣ 38.0
0.0 ∣ 3.7
on
0.8 ∣ 1.5
5.0 ∣ 5.3
0.0 ∣ 10.0
4.2 ∣ 52.1
0.0 ∣ 42.2
0.0 ∣ 4.8
google/gemma-4-E4B-it
off
4.2 ∣ 16.8
2.5 ∣ 3.3
5.8 ∣ 23.5
11.7 ∣ 69.4
2.5 ∣ 58.6
0.8 ∣ 12.7
on
4.2 ∣ 25.1
6.7 ∣ 7.9
9.2 ∣ 26.1
10.8 ∣ 71.4
0.0 ∣ 56.8
0.8 ∣ 16.2
google/gemma-4-26B-A4B-it
off
7.5 ∣ 43.2
2.5 ∣ 3.3
9.2 ∣ 35.5
15.0 ∣ 75.1
4.2 ∣ 64.5
1.7 ∣ 22.8
Appendix
Table 4: Analysis and evaluation tasks. Each cell reports complete-task success (%) ∣ task-native score ×100 .
Table 6: Complete-task success across structural-richness bands. Values are percentages.
Model
Reasoning
Formal.
Chain
Diagnosis
Status
Semantics
Perturb.
Gemma
google/gemma-4-E2B-it
off
2.5 ∣ 3.1
7.5 ∣ 8.4
15.0 ∣ 26.2
5.0 ∣ 56.0
0.0 ∣ 40.2
0.0 ∣ 8.2
on
2.5 ∣ 4.6
15.0 ∣ 15.7
0.0 ∣ 16.1
12.5 ∣ 65.2
0.0 ∣ 47.3
0.0 ∣ 9.1
google/gemma-4-E4B-it
off
12.5 ∣ 32.0
5.0 ∣ 5.0
17.5 ∣ 50.7
35.0 ∣ 81.5
7.5 ∣ 71.0
2.5 ∣ 28.0
on
12.5 ∣ 35.3
15.0 ∣ 16.7
27.5 ∣ 54.4
32.5 ∣ 84.8
0.0 ∣ 62.1
2.5 ∣ 30.7
google/gemma-4-26B-A4B-it
off
20.0 ∣ 49.0
7.5 ∣ 7.5
27.5 ∣ 73.8
42.5 ∣ 86.9
12.5 ∣ 75.2
5.0 ∣ 37.5
Appendix
Table 7: Task-specific analysis/evaluation performance for curriculum configurations L1–L5. Each cell reports complete-task success (%) ∣ task-native score ×100 .
Model
Reasoning
Pref.
Counter
Counter+S
Attack
Defence
Attack–Def.
Gemma
google/gemma-4-E2B-it
off
7.5 ∣ 8.2
0.0 ∣ 0.1
0.0 ∣ 0.2
0.0 ∣ 2.2
2.5 ∣ 2.5
0.0 ∣ 1.4
on
10.0 ∣ 10.0
0.0 ∣ 0.4
0.0 ∣ 0.6
0.0 ∣ 3.1
7.5 ∣ 7.5
0.0 ∣ 1.9
google/gemma-4-E4B-it
off
30.0 ∣ 31.8
0.0 ∣ 4.8
0.0 ∣ 4.4
0.0 ∣ 7.0
5.0 ∣ 5.0
0.0 ∣ 3.9
on
20.0 ∣ 21.4
0.0 ∣ 3.6
0.0 ∣ 5.8
0.0 ∣ 6.9
12.5 ∣ 12.5
0.0 ∣ 5.2
google/gemma-4-26B-A4B-it
off
42.5 ∣ 43.2
7.5 ∣ 10.2
5.0 ∣ 8.0
0.0 ∣ 8.5
32.5 ∣ 32.5
7.5 ∣ 13.9
Appendix
Table 8: Task-specific constructive performance for curriculum configurations L1–L5. Each cell reports complete-task success (%) ∣ task-native score ×100 .
Model
Reasoning
Formal.
Chain
Diagnosis
Status
Semantics
Perturb.
Gemma
google/gemma-4-E2B-it
off
0.0 ∣ 0.0
0.0 ∣ 1.8
0.0 ∣ 6.4
0.0 ∣ 44.6
0.0 ∣ 36.2
0.0 ∣ 2.6
on
0.0 ∣ 0.0
0.0 ∣ 0.2
0.0 ∣ 7.1
0.0 ∣ 47.8
0.0 ∣ 39.9
0.0 ∣ 2.7
google/gemma-4-E4B-it
off
0.0 ∣ 2.4
2.5 ∣ 4.0
0.0 ∣ 11.7
0.0 ∣ 67.8
0.0 ∣ 54.0
0.0 ∣ 6.9
on
0.0 ∣ 15.2
2.5 ∣ 3.8
0.0 ∣ 13.2
0.0 ∣ 70.7
0.0 ∣ 55.6
0.0 ∣ 10.5
google/gemma-4-26B-A4B-it
off
2.5 ∣ 40.8
0.0 ∣ 0.0
0.0 ∣ 22.2
2.5 ∣ 72.2
0.0 ∣ 57.1
0.0 ∣ 20.6
Appendix
Table 9: Task-specific analysis/evaluation performance for curriculum configurations L6–L10. Each cell reports complete-task success (%) ∣ task-native score ×100 .
Model
Reasoning
Pref.
Counter
Counter+S
Attack
Defence
Attack–Def.
Gemma
google/gemma-4-E2B-it
off
0.0 ∣ 0.0
0.0 ∣ 0.0
0.0 ∣ 0.0
0.0 ∣ 0.4
0.0 ∣ 0.0
0.0 ∣ 0.4
on
0.0 ∣ 0.4
0.0 ∣ 0.2
0.0 ∣ 0.0
0.0 ∣ 0.4
0.0 ∣ 0.0
0.0 ∣ 0.6
google/gemma-4-E4B-it
off
5.0 ∣ 6.8
0.0 ∣ 1.4
0.0 ∣ 0.9
0.0 ∣ 2.6
2.5 ∣ 4.5
0.0 ∣ 2.1
on
2.5 ∣ 7.4
0.0 ∣ 2.6
0.0 ∣ 2.5
0.0 ∣ 3.3
0.0 ∣ 1.7
2.5 ∣ 6.2
google/gemma-4-26B-A4B-it
off
27.5 ∣ 30.9
0.0 ∣ 2.1
2.5 ∣ 5.8
0.0 ∣ 3.6
20.0 ∣ 20.7
12.5 ∣ 17.9
Appendix
Table 10: Task-specific constructive performance for curriculum configurations L6–L10. Each cell reports complete-task success (%) ∣ task-native score ×100 .
Model
Reasoning
Formal.
Chain
Diagnosis
Status
Semantics
Perturb.
Gemma
google/gemma-4-E2B-it
off
0.0 ∣ 0.0
0.0 ∣ 0.3
0.0 ∣ 6.7
0.0 ∣ 42.1
0.0 ∣ 37.7
0.0 ∣ 0.5
on
0.0 ∣ 0.0
0.0 ∣ 0.0
0.0 ∣ 6.7
0.0 ∣ 43.4
0.0 ∣ 39.5
0.0 ∣ 2.5
google/gemma-4-E4B-it
off
0.0 ∣ 15.9
0.0 ∣ 0.8
0.0 ∣ 8.2
0.0 ∣ 59.0
0.0 ∣ 50.7
0.0 ∣ 3.3
on
0.0 ∣ 24.9
2.5 ∣ 3.3
0.0 ∣ 10.7
0.0 ∣ 58.6
0.0 ∣ 52.8
0.0 ∣ 7.5
google/gemma-4-26B-A4B-it
off
0.0 ∣ 39.8
0.0 ∣ 2.3
0.0 ∣ 10.6
0.0 ∣ 66.2
0.0 ∣ 61.2
0.0 ∣ 10.2
Appendix
Table 11: Task-specific analysis/evaluation performance for curriculum configurations L11–L15. Each cell reports complete-task success (%) ∣ task-native score ×100 .
Model
Reasoning
Pref.
Counter
Counter+S
Attack
Defence
Attack–Def.
Gemma
google/gemma-4-E2B-it
off
0.0 ∣ 0.0
0.0 ∣ 0.0
0.0 ∣ 0.0
0.0 ∣ 0.1
0.0 ∣ 0.0
0.0 ∣ 0.1
on
0.0 ∣ 0.0
0.0 ∣ 0.0
0.0 ∣ 0.0
0.0 ∣ 0.1
0.0 ∣ 0.0
0.0 ∣ 0.4
google/gemma-4-E4B-it
off
2.5 ∣ 5.5
0.0 ∣ 0.2
0.0 ∣ 0.0
0.0 ∣ 2.2
0.0 ∣ 4.0
0.0 ∣ 1.1
on
2.5 ∣ 6.0
0.0 ∣ 0.8
0.0 ∣ 2.4
0.0 ∣ 2.3
0.0 ∣ 6.3
0.0 ∣ 3.5
google/gemma-4-26B-A4B-it
off
22.5 ∣ 26.2
0.0 ∣ 2.2
5.0 ∣ 6.7
0.0 ∣ 0.8
10.0 ∣ 13.2
10.0 ∣ 13.8
Appendix
Table 12: Task-specific constructive performance for curriculum configurations L11–L15. Each cell reports complete-task success (%) ∣ task-native score ×100 .
Model
Reasoning
Last-link
Weakest-link
Democratic
Elitist
Gemma
google/gemma-4-E2B-it
off
1.0
1.2
1.4
0.8
on
1.5
1.1
1.2
1.4
google/gemma-4-E4B-it
off
5.1
1.9
3.9
3.2
on
4.9
2.6
3.9
3.6
google/gemma-4-26B-A4B-it
off
14.0
4.0
9.3
8.8
Appendix
Table 13: Performance by argument and set ordering. Values are complete-task success (%). Last-link and weakest-link refer to the argument comparison principle; democratic and elitist refer to the set ordering used for preference comparison.
Model
Reasoning
Formal.
Chain
Diagnosis
Status
Semantics
Perturb.
Gemma
google/gemma-4-E2B-it
off
0.0 ∣ 1.7
0.0 ∣ 5.0
5.0 ∣ 5.0
0.0 ∣ 3.3
0.0 ∣ 0.0
0.0 ∣ 0.0
on
0.0 ∣ 1.7
3.3 ∣ 6.7
0.0 ∣ 0.0
3.3 ∣ 5.0
0.0 ∣ 0.0
0.0 ∣ 0.0
google/gemma-4-E4B-it
off
5.0 ∣ 3.3
3.3 ∣ 1.7
6.7 ∣ 5.0
13.3 ∣ 10.0
3.3 ∣ 1.7
0.0 ∣ 1.7
on
5.0 ∣ 3.3
5.0 ∣ 8.3
10.0 ∣ 8.3
11.7 ∣ 10.0
0.0 ∣ 0.0
1.7 ∣ 0.0
google/gemma-4-26B-A4B-it
off
10.0 ∣ 5.0
3.3 ∣ 1.7
10.0 ∣ 8.3
15.0 ∣ 15.0
3.3 ∣ 5.0
3.3 ∣ 0.0
Appendix
Table 14: Task-specific last-link versus weakest-link performance on analysis/evaluation tasks. Each cell reports complete-task success as last-link (%) ∣ weakest-link (%).
Model
Reasoning
Pref.
Counter
Counter+S
Attack
Defence
Attack–Def.
Gemma
google/gemma-4-E2B-it
off
5.0 ∣ 0.0
0.0 ∣ 0.0
0.0 ∣ 0.0
0.0 ∣ 0.0
1.7 ∣ 0.0
0.0 ∣ 0.0
on
6.7 ∣ 0.0
0.0 ∣ 0.0
0.0 ∣ 0.0
0.0 ∣ 0.0
5.0 ∣ 0.0
0.0 ∣ 0.0
google/gemma-4-E4B-it
off
25.0 ∣ 0.0
0.0 ∣ 0.0
0.0 ∣ 0.0
0.0 ∣ 0.0
5.0 ∣ 0.0
0.0 ∣ 0.0
on
16.7 ∣ 0.0
0.0 ∣ 0.0
0.0 ∣ 0.0
0.0 ∣ 0.0
8.3 ∣ 0.0
0.0 ∣ 1.7
google/gemma-4-26B-A4B-it
off
61.7 ∣ 0.0
3.3 ∣ 1.7
3.3 ∣ 5.0
0.0 ∣ 0.0
35.0 ∣ 6.7
20.0 ∣ 0.0
Appendix
Table 15: Task-specific last-link versus weakest-link performance on constructive tasks. Each cell reports complete-task success as last-link (%) ∣ weakest-link (%).
Model
Reasoning
Trunc.
No answer
Compliance
Canonical
Cond.
Δ
Gemma
google/gemma-4-E2B-it
off
0.4
0.8
99.2
1.1
1.1
+0.0
on
0.1
20.9
79.1
1.3
1.7
+0.3
google/gemma-4-E4B-it
off
0.0
0.2
99.8
3.5
3.5
+0.0
on
0.1
4.2
95.8
3.8
3.9
+0.2
google/gemma-4-26B-A4B-it
off
10.3
9.9
90.1
9.0
10.0
+1.0
Appendix
Table 16: Generation and answer-protocol diagnostics. Trunc. is the percentage of truncated generations; No answer is the percentage without the required <answer> region; Compliance is the corresponding answer-region compliance rate. Cond. denotes success conditioned on the presence of an answer region, and Δ is conditioned minus canonical success in percentage points.
Defeasible reasoning is a type of reasoning where inferences are drawn from plausible current evidence, but can be retracted upon the introduction of newer evidence. Although recent studies have examined language-model behaviors in defeasible reasoning, the datasets have been static and lack wide coverage of non-monotonic reasoning categories. We introduce DeReLab, a generative framework that produces multi-turn belief-updating conversations from parameterized graph structures across default and inheritance reasoning, with formally verified ground truth at every turn, enabling controlled measurement of how models respond to confirming and disconfirming evidence. This controlled generation process creates a testbed for experimental designs that isolate specific reasoning demands. Applying this capability to the study of confirmation bias, we evaluate nine open and proprietary large language models and find that nearly all exhibit a systematic tendency to accept congruent evidence while resisting incongruent updates, with several models correctly identifying a weakening update yet failing to revise their conclusion. We believe our work and findings will facilitate future research on evaluating language models in defeasible reasoning.
Jayanta Sadhu, Sayem Shahad, Kenneth Marino
University of Utah · Bangladesh University of Engineering and Technology
Evaluating large language models (LLMs) on natural-language logical reasoning is essential because rule-governed tasks require conclusions to follow strictly from stated premises. Many existing logical-reasoning benchmarks are generated by templating natural-language items from sampled formulas, provide only coarse or unaudited formal annotations, and are now quickly saturated by frontier reasoning models. We present LLMEval-Logic, a Chinese logical reasoning benchmark built from realistic situational scenarios. Its pipeline forward-authors and expert-audits natural-language items together with their reference formalizations, verifies annotated answers with Z3, constructs expert rubrics for natural-to-formal grading, and hardens selected items through a closed-loop adversarial workflow. The benchmark is released in two paired subsets: a 246-item Base subset shipped with 1,400 expert-developed rubric atoms, and a 190-item Hard subset with 938 multi-step sub-questions over closed model spaces. Evaluating 14 frontier LLMs on LLMEval-Logic reveals substantial gaps in current models: the best model reaches only 37.5% Hard Item Accuracy, and even with reference symbols the highest joint Z3+Rubric formalization score among evaluated models reaches only 60.16%. Our benchmark is publicly available at https://github.com/llmeval/LLMEval-Logic.
Ming Zhang, Qiyuan Peng, Yinxi Wei +13
Institute of Trustworthy Embodied Artificial Intelligence, Fudan University · 2Hunyuan Team, Tencent · School of Philosophy, Fudan University
A rule-based logic solver resolves every instance in our benchmark in under 50 microseconds with 100% accuracy; the best frontier language model reaches 65% at best and drops to 23.5% under rendering-robust evaluation (worst case over four surface renderings). We introduce DeFAb (Defeasible Abduction Benchmark), a dataset and generation pipeline that converts four decades of publicly funded knowledge bases into formally grounded instances for defeasible abduction: constructing hypotheses that explain anomalies by overriding defaults while preserving unrelated expectations. Because every hypothesis must pass polynomial-time checks for valid derivation, conservativity, and minimality, DeFAb makes logical rigor the instrument for measuring creativity and theoretical reasoning, scoring the disciplined construction of theory revisions rather than fluent but theory-destroying prose. The pipeline pairs taxonomic hierarchies (OpenCyc, YAGO, Wikidata) with behavioral property graphs (ConceptNet, UMLS) to produce 372,648+ instances across 33.75M materialized rules from 18 sources, in three levels with polynomial-time verifiable gold standards. Four frontier models do not reliably internalize defeasible reasoning: rendering-robust Level 2 accuracy is 7.8-23.5%; chain-of-thought variance (~36 pp) exceeds any inter-model gap; and a matched contamination control isolates a +19.4 pp Level 3 gap. We further release DeFAb-Hard (a 235-instance Level 3 difficulty variant; best model 53.3% vs 100% symbolic) and CONJURE (a kernel-verified transformative-creativity variant of 560 Lean 4/Mathlib instances whose gold answers are definitions the proof kernel did not previously contain, judge-free verifier; a pilot finds zero novel concepts). The same verifier doubles as an exact reward for preference optimization (DPO, RLVR/GRPO). Released under MIT at https://huggingface.co/datasets/PatrickAllenCooper/DeFAb.