{"path":"research/one-inference-per-link/report-datasets-and-historical-cases.md","content":"# Research report: labelled reasoning-step datasets and historical hidden-premise cases\n\n*A research helper's report (Sonnet), 2026-10-24, saved verbatim for `../one-inference-per-link.md`. Its brief: public datasets labelling natural-language reasoning steps valid or invalid, and real historical cases where a published inference hid a premise later identified as the flaw. Read-status tags are the helper's own.*\n\n---\n\nREPORT: labelled reasoning-step datasets (A) and historical hidden-premise cases (B)\n\nRead-status tags: [FULL] read in full, [PART] part of the text read, [ABS] abstract or search snippet only, [SEC] secondary source. I quote only short dataset items and paraphrase papers elsewhere. Extracted paper text (REVEAL, EntailmentBank, ROSCOE, METGEN, Becker, England 2007, Morabia) is in /private/tmp/claude-501/-Users-fredrikbranstrom-Projects-deliberus/a4c8e48a-9cad-460d-92d3-43f20d6c7339/scratchpad/pdfs/*.txt if you want to re-check.\n\n## Bottom line for part A\n\n1. **Most usable for \"is this one step a single inference from its stated premises\" on non-math text:**\n   - EntailmentBank: valid single steps only, so you must build the negatives.\n   - METGEN's four-way step labels: the right label scheme, but I could not confirm the labels are released.\n   - REVEAL: real human labels on model steps, but gated, test-only, and CC-BY-ND.\n2. **Math-only step-label sets** (PRM800K, ProcessBench) are big and open but unsuited to your NLI check on text.\n3. **Missing-premise argument corpora** are small. Becker et al. gives the gold text of the missing premise for 719 pairs, but I could not confirm where it is hosted.\n\n## A. Datasets\n\n**A1. EntailmentBank**\n- **Paper:** Dalvi, Jansen, Tafjord, Xie, Smith, Pipatanangkura, Clark. \"Explaining Answers with Entailment Trees\", EMNLP 2021, https://arxiv.org/abs/2104.08661 [PART]. Authors beyond the first are from memory, not checked.\n- **Download:** the repo README says \"Dataset available at https://allenai.org/data/entailmentbank\". That URL returns a 307 redirect to a Google Drive folder: https://drive.google.com/drive/folders/1YjjeZy9FEbXh-84-HjqOu8Rfve9oj1Te [redirect seen, folder not opened]. Code is at https://github.com/allenai/entailment_bank [PART].\n- **Mirror:** the METGEN repo (https://github.com/Raising-hrx/MetGen) says its `data/entailment_trees_emnlp2021_data_v2` is the EntailmentBank data \"downloaded from AllenAI\".\n- **Licence:** the code repo is Apache-2.0. I could not confirm a licence for the data. Treat it as unknown.\n- **Size [FULL for these facts]:**\n  - 1,840 trees (train 1,313, dev 187, test 340).\n  - 5,881 \"discrete entailment steps\" (train 4,175, dev 597, test 1,109).\n  - 7.6 nodes and 3.2 steps per tree on average; a step typically involves 3 facts (two leaves entailing a conclusion).\n  - Half the trees have 1–2 steps.\n- **Label meaning:** every step is gold-valid. The authors' stated goal is \"a single inference\" per step (a single taxonomic inference, a conjunction of two facts, or one rule application). Steps were authored by three trained annotators and reviewed by a different author. There are **no invalid-step labels**.\n- **Domain:** grade-school science, from ARC questions and the WorldTree V2 corpus.\n- **Sample step, verbatim from their Table 3 (inference type \"Substitution\", 42% of 100 sampled steps; \"Inference from Rule\" is 33%):**\n  - s1 \"when a light wave hits a reflective object, the light wave will be reflected\"\n  - s2 \"a mirror is a kind of reflective object\"\n  - int \"when a light wave hits a mirror, the light wave will be reflected\"\n- **Use for you:**\n  - It is the cleanest source of positives.\n  - Negatives come from three routes:\n    - Delete one premise to make a \"missing premise\" item.\n    - Swap in a premise from another tree.\n    - Apply the 12 perturbation rules that ROSCOE already applied to this dataset (A4).\n  - Section 6.3.1 of the paper analysed 100 model-generated steps from imperfect trees. The largest failure class, 47%, was \"invalid entailment\": the model used knowledge that was not in that step's inputs but was elsewhere in the context. That is exactly your leap pattern, and it gives you the shape of a negative to construct.\n\n**A2. REVEAL**\n- **Paper:** Jacovi, Bitton, Bohnet, Herzig, Honovich, Tseng, Collins, Aharoni, Geva. \"A Chain-of-Thought Is as Strong as Its Weakest Link: A Benchmark for Verifiers of Reasoning Chains\", ACL 2024, https://arxiv.org/abs/2402.00559 [FULL text extracted; read the dataset sections].\n- **Data:** https://huggingface.co/datasets/google/reveal [ABS, dataset card read]. Project page: reveal-dataset.github.io.\n- **Licence and access:** the card says cc-by-nd-4.0. It is **gated** (log in and accept conditions), meant as a test set only, and must not be posted where web crawlers can reach it. The ND clause plausibly rules out derivative variants.\n- **Size (paper Table 1, REVEAL-Eval):**\n  - 704 questions and 1,002 chains.\n  - 3,360 steps.\n  - 1,250 logic steps, of which 1,063 are logically correct, so about 187 are incorrect (my arithmetic).\n  - Plus REVEAL-Open: 205 questions, 224 chains, 847 steps, 306 logic steps, held out for low agreement.\n- **Where the chains come from:** Flan-PaLM-540B, GPT-3 text-davinci-003 and Flan-UL2-20B answering StrategyQA, MuSiQue, Sports Understanding and Fermi questions.\n- **Label meaning:** each step is first marked relevant or not, then typed as attribution (a factual claim), logic, or both.\n  - Logic steps are \"correct\" if they can be inferred from the question and previous steps, otherwise \"incorrect\".\n  - A logic step after an incorrect one is \"undefined\".\n  - Attribution steps are checked against retrieved Wikipedia passages.\n  - Every label has five free-text justifications.\n  - Krippendorff's alpha is 0.46 for logic steps and 0.49 for attribution.\n  - 87.5% of logic steps are correct and 18.5% of chains contain an incorrect logic step.\n- **Sample from the paper's Fig. 3/4:**\n  - The question asks whether an art dealer could buy a Boeing 737-800 with a Da Vinci painting.\n  - Step 3 reads \"Thus, an art dealer would not be able to buy a Boeing 737-800 with a Da Vinci painting.\"\n  - It is labelled logically incorrect, with the justification that the inference rests on the painting selling for millions, so it may still sell for more than the price of a 737 (justification text garbled in extraction).\n- **Use for you:**\n  - These are real human step judgments on non-math text, including leaps. The logic steps are few (about 187 incorrect) and borderline cases are common.\n  - The label is \"correct given previous steps\", which is not quite \"single inference\".\n  - Fine as a held-out check, not a training or derivative source.\n\n**A3. METGEN step labels (the closest label scheme to yours)**\n- **Paper:** Hong, Zhang, Yu, Zhang (Raising-hrx). \"METGEN: A Module-Based Entailment Tree Generation Framework for Answer Explanation\", Findings of NAACL 2022, https://arxiv.org/abs/2205.02593 [PART, manual-evaluation section read].\n- **Labels:** three student experts labelled each generated step as one of four.\n  - Valid: the conclusion can be inferred from the premises and does not trivially repeat them.\n  - Unsupported: it conflicts with, is irrelevant to, or does not follow from the premises.\n  - Repeat premises: the conclusion trivially repeats one or more premises.\n  - Missing premises: the conclusion uses knowledge not stated in the premises; the step would be correct if one more premise were added.\n- **Agreement:** Cohen's kappa 0.85 for steps and 0.76 for trees.\n- **Reported numbers:** 17% of the EntailmentWriter baseline's steps were \"missing premises\", versus about 2% for METGEN. Valid-step share rose from 38% to 70%.\n- **Release:** the repo (https://github.com/Raising-hrx/MetGen, Apache-2.0) has a `Steps` data folder described as \"annotated/pseudo step data for module training\", and processed data on an external Tsinghua cloud link. I **could not confirm** that the per-step validity annotations are released. The paper gives aggregate percentages only.\n- **Use for you:** adopt the label definitions as your spec. Email the authors for the labels.\n\n**A4. ROSCOE annotations**\n- **Paper:** Golovneva, Chen, Poff, Corredor, Zettlemoyer, Fazel-Zarandi, Celikyilmaz. \"ROSCOE: A Suite of Metrics for Scoring Step-by-Step Reasoning\", ICLR 2023, https://arxiv.org/abs/2212.07919 [PART].\n- **Data:** annotated datasets at https://dl.fbaipublicfiles.com/parlai/projects/roscoe/annotations.zip; code at https://github.com/facebookresearch/ParlAI/tree/main/projects/roscoe. I did not download it, so counts and licence are unchecked.\n- **Two kinds of data:**\n  - *Human-judged:* five expert annotators rated GPT-3 or chain-of-thought steps on GSM8K, DROP, e-SNLI, Cosmos-QA and SemEval-2018 commonsense. Each step is flagged for taxonomy errors: Grammar, Factuality, Hallucination, Redundancy, Repetition, Missing step, Coherency, Commonsense, Arithmetic. \"Missing step\" means the reasoning is incomplete and lacks information needed for the answer. \"Commonsense\" means a relation that should be known (their example is that ducks are birds) is lacking.\n  - *Diagnostic (synthetic):* 12 deterministic perturbation rules applied to EntailmentBank, ProofWriter, MATH, ASDiv, AQuA, EQASC and StrategyQA. Binary label perturbed or not. These are machine-made, not human.\n- **Use for you:** the human \"missing step / commonsense\" flags on e-SNLI and Cosmos-QA are worth extracting. The EntailmentBank perturbation code is a ready-made negative generator.\n\n**A5. PRM800K and ProcessBench (math, open)**\n- **PRM800K:** Lightman et al., \"Let's Verify Step by Step\", https://arxiv.org/abs/2305.20050 [ABS]; https://github.com/openai/prm800k [PART]. 800,000 step-level human labels on MATH solutions. Rating is -1, 0 or +1 (0 is a step that is not wrong but makes no progress). Labelling stopped at the first error in phase 2. MIT licence. The data is stored in Git LFS.\n- **ProcessBench:** Zheng et al. (Qwen team), https://arxiv.org/abs/2412.06559 [ABS]; https://huggingface.co/datasets/Qwen/ProcessBench [ABS]. 3,400 cases, Apache-2.0. Subsets: GSM8K 400, MATH, OlympiadBench, Omni-MATH, roughly 1,000 each. Each case has a first-error-step annotation by human experts. I did not confirm the exact meaning of the label field (my guess is the index of the first wrong step, with no-error coded separately).\n- **Use for you:** math only, and the check being tested here is NLI/embedding on prose. These are the largest \"real human step validity\" sets, so use them only if you want a numeric-domain control.\n\n**A6. Argument datasets with implicit premises or warrants**\n- **Becker, Korfhage, Frank.** \"Implicit Knowledge in Argumentative Texts: An Annotated Corpus\", LREC 2020, https://arxiv.org/abs/1912.10161 [PART].\n  - Pairs of argument units from the Microtexts corpus (Peldszus & Stede). Expert annotators wrote the short sentences that make the connection explicit (as few as possible, short and simple). A third expert adjudicated the gold.\n  - Size: 719 unit pairs and 1,295 inserted sentences, an average of 1.8 per pair.\n  - Sample (their Fig. 2): (a) \"Capital punishment is not a solution\" (b) \"as it cannot be ruled out that the judicial process may make mistakes.\" The inserted sentences are \"In a judicial process it is decided about capital punishment.\" and \"Mistakes don't lead to solutions.\"\n  - Release: the paper says it \"will be made public as an extension to the Microtext corpus\". I **could not find the download location**, nor the licence.\n  - Use for you: this is real human ground truth for what the missing premise is, which is good for testing whether NLI turns neutral to entailment once the premise is added. Positives only (no invalid-step labels).\n- **ARCT (Habernal, Wachsmuth, Gurevych, Stein).** \"The Argument Reasoning Comprehension Task: Identification and Reconstruction of Implicit Warrants\", NAACL 2018, https://arxiv.org/abs/1708.01425 [ABS]; https://github.com/UKPLab/argument-reasoning-comprehension-task [PART].\n  - About 2,000 arguments (from news-comment debates) with two candidate warrants each, one correct. Per-split counts were not found.\n  - Format: tab-separated fields for warrant0, warrant1, correct label (0 or 1), reason, claim, debate title.\n  - Sample: claim \"Miss America is good for women\"; reason that it gives scholarships; correct warrant \"scholarships would give women a chance to study\", the other \"scholarships would take women from the home\".\n  - Licence: the code is Apache-2.0, but the source texts are individually copyrighted by their authors; the README says to contact authors for permission.\n  - Caveat: Niven & Kao, ACL 2019, https://arxiv.org/abs/1907.07355 [ABS] show BERT reaches about 77% by exploiting spurious statistical cues, and they publish an adversarial version where models are at chance. Use their adversarial set, not the original.\n  - Use for you: it tests \"which of two stated rules licenses this step\", a coarse proxy.\n- **Boltužić & Šnajder.** \"Fill the Gap! Analyzing Implicit Premises between Claims from Online Debates\", ArgMining 2016, pp. 124–133, https://aclanthology.org/W16-2815 [ABS]. Annotators wrote premises with no guidelines, giving high variance; a later paper describes the data as small (125 claim pairs) [SEC]. Low value for you.\n- **ProofWriter** (Tafjord, Dalvi, Clark, https://arxiv.org/abs/2012.13048 [ABS]). Synthetic RuleTaker-style theories with machine-generated proofs, plus an abduction task for missing facts. No human step labels. Not suitable as real-case ground truth.\n- **Sprague, Bostrom, Chaudhuri, Durrett.** \"Natural Language Deduction with Incomplete Information\", EMNLP 2022, https://arxiv.org/abs/2211.00614 [ABS]. Abductive missing-premise generation on a modified EntailmentBank plus a new \"Everyday Norms: Why Not?\" set; code and data at https://github.com/Zayne-sprague/Natural_Language_Deduction_with_Incomplete_Information. I did not check whether it contains human validity labels.\n\n## B. Historical cases of a hidden premise in a published inference\n\nEach case gives the reasoning chain, the hidden premise, what exposed it, and sources. Cases 1, 2, 5, 6, 7 and 8 are well-sourced from what I read; 3, 4 and 9 are weaker and flagged.\n\n**B1. Lord Kelvin's age of the Earth (physical science)**\n- **Reasoning as held:** The Earth began molten and loses heat only by conduction through its rock. The measured surface temperature gradient, a rock-melting starting temperature and laboratory rock conductivity give a cooling time. Kelvin's 1863 calculation gave 96 million years, bounded at 24 and 400 million years; his last estimate in 1897 was 20–40 million years [England, Molnar & Richter 2007 [PART]; Wikipedia \"Age of the Earth\" [SEC]].\n- **Hidden premise:** The Earth is rigid and homogeneous, so heat in the interior moves only by conduction at the conductivity measured at the surface. Kelvin listed assumptions of rigidity, homogeneity and no undiscovered energy source.\n- **What exposed it:** John Perry (his former assistant) argued in Nature in 1895 that a fluid or partly fluid interior would carry heat by convection, which behaves like a very high conductivity, making the Earth far older (secondary sources give 2–3 billion years). England, Molnar & Richter (2007) show the popular story that radioactivity refuted Kelvin is wrong. Adding the known radioactivity to Kelvin's calculation does not overturn his conclusion; Perry's convection point was the real flaw and was forgotten.\n- **Sources:** England, P., Molnar, P., Richter, F. (2007), \"John Perry's neglected critique of Kelvin's age for the Earth\", GSA Today 17(1), https://rock.geosociety.org/net/gsatoday/archive/17/1/pdf/i1052-5173-17-1-4.pdf [PART, about 40% read]. Wikipedia https://en.wikipedia.org/wiki/Age_of_Earth [SEC]. Perry's 1895 Nature piece (https://www.nature.com/articles/051341b0.pdf) was not opened [ABS via search snippet].\n- **Note for tests:** this case has a tempting decoy hidden premise (\"no undiscovered heat source\") that is not the one that mattered.\n\n**B2. Farr's elevation law versus Snow's water-supply evidence (epidemiology)**\n- **Reasoning as held:** Under the miasma view, cholera spreads by foul air. Farr's 1852 report on the 1848–49 epidemic found cholera mortality fell as district elevation above the Thames rose, and he took elevation to be a major contributor to the disease [Wikipedia \"William Farr\" [SEC]; Morabia 2001 [FULL]].\n- **Hidden premise:** The elevation gradient acts through the air, i.e. nothing else that varies with elevation carries the effect.\n- **What exposed it:** Snow's 1855 comparison of customers of two water companies with intermingled pipes. In seven weeks of 1854, Southwark & Vauxhall had 1,263 deaths in 40,046 houses (315 per 10,000) and Lambeth, which had moved its intake to clean water, had 98 in 26,107 (37 per 10,000), with the rest of London at 59. Snow wrote that there was no difference in the houses or people supplied, so the only difference was the water [data8 chapter quoting Snow's table [PART]]. Morabia says Farr's law \"did not reflect causation\". Farr accepted Snow's explanation by 1866 [SEC].\n- **Not verified:** I did not find a source that low districts took more of their water from the polluted tidal Thames, so do not assert that as the mechanism.\n- **Sources:** Morabia, A. (2001), \"Snow and Farr: a scientific duet\", Soz.- Präventivmed. 46:223–224 (editorial quoting Snow 1855) [FULL; I read the PDF text]. https://en.wikipedia.org/wiki/William_Farr [SEC]. https://data8.datascience.uchicago.edu/chapters/02/2/snow-s-grand-experiment [PART].\n\n**B3. Tacoma Narrows Bridge, 1940 (engineering; weaker sourcing)**\n- **Reasoning as held:** The structure was checked against the static wind forces normally considered for suspension bridges, and a more slender, flexible deck was acceptable by contemporary theory, so it was safe.\n- **Hidden premise:** Wind acts on a bridge deck only as a static load; no wind-driven oscillation can feed energy into the structure.\n- **What exposed it:** The collapse, then the Carmody Board (Ammann, von Kármán, Woodruff; report 28 March 1941), which found the bridge sound against static forces and attributed the failure to wind-induced oscillation given extreme flexibility; it said aerodynamic forces were little understood and called for wind-tunnel model tests. Billah & Scanlan (1991) later argued the failure was self-excited aeroelastic oscillation rather than resonance as textbooks taught [summary only].\n- **Sources:** WSDOT history page https://wsdot.wa.gov/TNBhistory/bridges-failure.htm [PART]; search-result summary of the board report [SEC]; Billah & Scanlan, Am. J. Phys. 59 (1991) [ABS via secondary summaries]. I could not open the Caltech-hosted full report, and I did not verify any Moisseiff-specific premise or numbers.\n\n**B4. De Havilland Comet 1 (engineering; weaker sourcing, use with care)**\n- **Reasoning as held:** The forward fuselage was cycled through more than 16,000 pressurisation cycles in testing, equated to about 40,000 airline hours, windows were tested at 12 psi, and one window frame survived 100 psi [Wikipedia [PART]]. A slide deck I did not open (via a search snippet) says the designers and regulator believed a high static proof pressure (2P proof, 2.5P design) would protect against fatigue, since fatigue thresholds were known for steels but not thought to exist in aluminium alloys [ABS/SEC].\n- **Hidden premise:** The tested configuration and static margin represent the fatigue-critical details of the in-service airframe, and aluminium has a safe fatigue stress below which fatigue need not be assessed.\n- **What exposed it:** The Royal Aircraft Establishment water-tank test of airframe G-ALYU: it burst after 3,057 flight cycles (1,221 actual plus 1,836 simulated), with a crack starting at a bolt hole near the forward escape hatch cutout; the skin was too thin at countersunk holes and the frames did not arrest cracks. On G-ALYP, the crack began at a rivet hole near the rear ADF window. Passenger window shape was not a contributing factor [Wikipedia [PART, about the first 45% of the page]].\n- **Sources:** https://en.wikipedia.org/wiki/De_Havilland_Comet [SEC]. I could not confirm the proof-pressure belief from a primary source; the Court of Inquiry and RAE reports were not found.\n\n**B5. Birmingham Six and the Griess test (law)**\n- **Reasoning as held:** A positive Griess test on a swab of a man's hands means he had handled nitroglycerine-based explosive. Hill and Power tested positive. The forensic scientist Frank Skuse said he was 99% certain they had explosive traces (Wikipedia gives \"99%\"; some secondary sources say 98%). The trial judge preferred this to defence expert Hugh Black's dispute [Wikipedia [SEC]].\n- **Hidden premise:** The positive reaction is specific to nitroglycerine, with no innocent source.\n- **What exposed it:** Later gas chromatography/mass spectrometry tests were negative for Power and contradicted the initial positive for Hill. A later Forensic Science Service submission says nitrocellulose-containing items such as nitrocellulose-coated playing cards can also give positive Griess results. A Paul Foot article in the LRB reports that the judges conceded the test is not specific for nitroglycerine. The Court of Appeal quashed the convictions on 14 March 1991, saying the new scientific evidence \"throws grave doubt on Skuse's evidence, if it does not destroy it altogether\" and calling the convictions unsafe [Wikipedia quoting R v McIlkenny [1991]].\n- **Sources:** https://en.wikipedia.org/wiki/Birmingham_Six [PART, SEC]; https://www.lrb.co.uk/the-paper/v11/n23/paul-foot/inside-the-system [ABS via search summary]; the Forensic Science Service submission at https://publications.parliament.uk/pa/cm201011/cmselect/cmsctech/writev/forensic/m67.htm [ABS via search summary]. Other contested aspects of this case (police fabrication, confessions) are separate from the hidden premise above.\n\n**B6. Pre-2008 belief that national US house prices do not fall together (economics/finance)**\n- **Reasoning as held:** Two reasoners, one chain. (a) Bernanke, then chair of the White House Council of Economic Advisers, said in a 2005 CNBC interview that there had never been a decline in house prices on a nationwide basis, and called a national fall unlikely (date is 1 July or 29 July 2005 depending on the source; wording varies between \"housing prices\" and \"house prices\") [Calculated Risk blog, Credit Writedowns/Mises transcripts: ABS/SEC]. (b) Commentators describe investors, rating agencies and regulators as believing that geographically diverse mortgage pools protected against price declines, because regional markets were not closely linked [SEC].\n- **Hidden premise:** Regional price changes stay weakly correlated in a downturn, so a pooled geographic mix cannot lose across the board. Correlations measured in normal times hold in the stressed state.\n- **What exposed it:** Miles (2015) found regional home-price correlations were often low in normal times, but \"regional correlations indeed rose dramatically during the latest downturn\", sometimes to unprecedented levels, reflecting contagion rather than ordinary interdependence. Estimates made in normal times can understate risk.\n- **Sources:** Miles, W. (2015), \"Contagion versus Interdependence Across Regional U.S. Housing Markets and Implications for RMBS Geographic Diversification Strategy\", J. Real Estate Portfolio Management 21(1):33–52, https://ideas.repec.org/a/taf/repmxx/v21y2015i1p33-52.html [ABS]; https://calculatedriskblog.com/2005/07/bernanke-house-prices-unlikely-to.html [ABS]. I could not retrieve the Financial Crisis Inquiry Commission report's own wording, so the rating-agency half rests on secondary summaries.\n\n**B7. Literary Digest poll, 1936 (statistics)**\n- **Reasoning as held:** The magazine polled ten million people (2.38 million answered) and predicted Landon at 57.08% and 370 electoral votes. Roosevelt actually won with 60.8% and 523 electoral votes. The very large sample size was taken to guarantee accuracy.\n- **Hidden premise:** The people who answered a mailing built from its own readers, automobile registrations and telephone lists, represent the voting electorate.\n- **What exposed it:** Squire (1988) used a 1937 Gallup survey asking respondents whether they had taken part in the Digest poll and concluded that both the sampling frame and non-response jointly produced the error; non-response bias, with strong Roosevelt opponents more likely to reply, was the primary contributor to the magnitude of the error. He estimated that had everyone who got a ballot replied, the Digest would have predicted Roosevelt. Lusinchi (2012) disputes the popular telephone-and-car explanation, and one critique notes Squire's Gallup data used quota methodology.\n- **Sources:** Squire, P. (1988), Public Opinion Quarterly 52(1):125–133 [ABS via secondary summaries]; https://en.wikipedia.org/wiki/The_Literary_Digest [SEC]; Lusinchi (2012), Social Science History [ABS via secondary summary].\n\n**B8. Robinson's ecological correlations (social science)**\n- **Reasoning as held:** A pattern across aggregate units, such as states, is read as a pattern among the individuals in them. The classic published instance is Durkheim's reading of Protestant localities having higher suicide rates as meaning Protestants have higher suicide risk (Wikipedia notes that critics treat this as an ecological fallacy).\n- **Hidden premise:** The relation between aggregate averages equals the relation between the same attributes within individuals.\n- **What exposed it:** Robinson (1950, American Sociological Review 15(3):351–357) used 1930 census data. Across states, the correlation between share foreign-born and illiteracy was about -0.53 (states with more immigrants were more literate; a 2011 correction gives -0.46), but at the individual level it was about +0.12 (immigrants were on average more likely to be illiterate). The reason: immigrants settled in states with more literate natives. Robinson explicitly warned against inferring individual behaviour from ecological correlations. The label \"ecological fallacy\" came later (Selvin 1958).\n- **Sources:** https://en.wikipedia.org/wiki/Ecological_fallacy [SEC]; figures cross-checked in a search summary citing Robinson [ABS]. I did not open Robinson's paper.\n\n**B9. Peptic ulcers and the sterile stomach (medicine; optional, weaker sourcing)**\n- **Reasoning as held:** Stomach acid is strong enough that no bacteria can survive in it, so ulcers are caused by excess acid, stress or diet rather than infection.\n- **Hidden premise:** Acid in the lumen means no bacteria anywhere in the stomach.\n- **What exposed it:** Marshall and Warren's work on *Helicobacter pylori*, which they proposed survives under the pH-neutral mucus layer, and Marshall's 1985 self-infection experiment, which produced stomach inflammation. A bacterial theory dating to about 1899 had been rejected on the acid argument.\n- **Sources:** secondary summaries (Penn State profile, MJA 2005 Nobel commentary, Britannica) [ABS/SEC]; I could not read Marshall's Nobel lecture text.\n\n## Cautions for your tests\n- **Premise-identity risk:** in B1 and B6 the folk story and the documented hidden premise differ, which is a good adversarial item but needs care with the \"gold\" premise sentence.\n- **Authorship of the chain:** B2 (Farr) and B8 are inference patterns whose exact original sentences I did not read; the chains above are my restatement from the cited secondary sources. If you need verbatim original reasoning, B1 (Perry's 1895 paper is cited and quoted within England 2007) and B5 are the most promising to source further, and B7 if you obtain Squire (1988).\n- **Reliability ranking:** best sourced are B1, B2, B5, B7. B3, B4 and B9 rest on secondary or snippet-level reading and should not be used as ground truth without checking the primary sources.\n"}