Fixing FOLIO and MALLS: Verified Annotations and an LLM-assisted Framework to Focus Human Relabeling
Paper • 2606.02837 • Published
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The dataset generation failed
Error code: DatasetGenerationError
Exception: CastError
Message: Couldn't cast
story_id: int64
Rel: struct<InThisClub: struct<arity: int64, pos_meaning: string, neg_meaning: string>, PerformOftenIn: s (... 30350 chars omitted)
child 0, InThisClub: struct<arity: int64, pos_meaning: string, neg_meaning: string>
child 0, arity: int64
child 1, pos_meaning: string
child 2, neg_meaning: string
child 1, PerformOftenIn: struct<arity: int64, pos_meaning: string, neg_meaning: string>
child 0, arity: int64
child 1, pos_meaning: string
child 2, neg_meaning: string
child 2, Attend: struct<arity: int64, pos_meaning: string, neg_meaning: string>
child 0, arity: int64
child 1, pos_meaning: string
child 2, neg_meaning: string
child 3, VeryEngagedWith: struct<arity: int64, pos_meaning: string, neg_meaning: string>
child 0, arity: int64
child 1, pos_meaning: string
child 2, neg_meaning: string
child 4, InActive: struct<arity: int64, pos_meaning: string, neg_meaning: string>
child 0, arity: int64
child 1, pos_meaning: string
child 2, neg_meaning: string
child 5, Disinterested: struct<arity: int64, pos_meaning: string, neg_meaning: string>
child 0, arity: int64
child 1, pos_meaning: string
child 2, neg_meaning: string
child 6, MemberOf: struct<arity: int64, pos_meaning: string, neg_meaning: string>
child 0, arity: int64
child 1, pos_meaning: string
child 2, neg_meaning: string
child 7, Chaperone: struct<arity: int64, pos_meaning: stri
...
: string
child 246, animal: string
child 247, daniShapiro: string
child 248, familyHistory: string
child 249, familySecrets: string
child 250, yr2003: string
child 251, boston: string
child 252, america: string
child 253, jumpShot: string
child 254, legMuscle: string
child 255, yuri: string
child 256, steinhauer: string
child 257, duMaurierClassic: string
child 258, year1992: string
child 259, descampe: string
child 260, belgium: string
child 261, jane: string
child 262, kiki: string
child 263, library: string
child 264, computerScienceDepartment: string
child 265, university: string
child 266, databaseCourse: string
child 267, professorDavid: string
child 268, lab: string
child 269, george: string
child 270, heinrichSchmidt: string
child 271, prussianStateParliament: string
child 272, naziReichstag: string
child 273, ailtonSilva: string
child 274, ailton: string
child 275, year1995: string
child 276, braga: string
child 277, nautico: string
child 278, fluminense: string
id: string
NLI_requires_more_info: string
label_old: string
ambiguity_commentary: string
amniguity_explanation: string
label_z3: string
note: string
FOL_sentence_old: string
label_new: string
label_mismatch_explanation: string
corrected: string
label: string
FOL_sentence: string
correction_explanation: string
ambiguity: bool
ambiguity_explanation: string
corerection_explanation: string
label_old_z3: string
correction: string
NL_sentence: string
to
{'id': Value('string'), 'NL_sentence': Value('string'), 'FOL_sentence': Value('string'), 'corrected': Value('string'), 'ambiguity': Value('bool'), 'ambiguity_explanation': Value('string'), 'correction_explanation': Value('string'), 'FOL_sentence_old': Value('string'), 'label': Value('string'), 'label_old': Value('string'), 'label_old_z3': Value('string'), 'label_z3': Value('string'), 'note': Value('string'), 'correction': Value('string'), 'label_new': Value('string'), 'NLI_requires_more_info': Value('string'), 'ambiguity_commentary': Value('string'), 'corerection_explanation': Value('string'), 'label_mismatch_explanation': Value('string'), 'amniguity_explanation': Value('string')}
because column names don't match
Traceback: Traceback (most recent call last):
File "/usr/local/lib/python3.12/site-packages/datasets/builder.py", line 1816, in _prepare_split_single
for key, table in generator:
^^^^^^^^^
File "/usr/local/lib/python3.12/site-packages/datasets/packaged_modules/json/json.py", line 310, in _generate_tables
self._cast_table(pa_table, json_field_paths=json_field_paths),
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/usr/local/lib/python3.12/site-packages/datasets/packaged_modules/json/json.py", line 130, in _cast_table
pa_table = table_cast(pa_table, self.info.features.arrow_schema)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/usr/local/lib/python3.12/site-packages/datasets/table.py", line 2369, in table_cast
return cast_table_to_schema(table, schema)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/usr/local/lib/python3.12/site-packages/datasets/table.py", line 2297, in cast_table_to_schema
raise CastError(
datasets.table.CastError: Couldn't cast
story_id: int64
Rel: struct<InThisClub: struct<arity: int64, pos_meaning: string, neg_meaning: string>, PerformOftenIn: s (... 30350 chars omitted)
child 0, InThisClub: struct<arity: int64, pos_meaning: string, neg_meaning: string>
child 0, arity: int64
child 1, pos_meaning: string
child 2, neg_meaning: string
child 1, PerformOftenIn: struct<arity: int64, pos_meaning: string, neg_meaning: string>
child 0, arity: int64
child 1, pos_meaning: string
child 2, neg_meaning: string
child 2, Attend: struct<arity: int64, pos_meaning: string, neg_meaning: string>
child 0, arity: int64
child 1, pos_meaning: string
child 2, neg_meaning: string
child 3, VeryEngagedWith: struct<arity: int64, pos_meaning: string, neg_meaning: string>
child 0, arity: int64
child 1, pos_meaning: string
child 2, neg_meaning: string
child 4, InActive: struct<arity: int64, pos_meaning: string, neg_meaning: string>
child 0, arity: int64
child 1, pos_meaning: string
child 2, neg_meaning: string
child 5, Disinterested: struct<arity: int64, pos_meaning: string, neg_meaning: string>
child 0, arity: int64
child 1, pos_meaning: string
child 2, neg_meaning: string
child 6, MemberOf: struct<arity: int64, pos_meaning: string, neg_meaning: string>
child 0, arity: int64
child 1, pos_meaning: string
child 2, neg_meaning: string
child 7, Chaperone: struct<arity: int64, pos_meaning: stri
...
: string
child 246, animal: string
child 247, daniShapiro: string
child 248, familyHistory: string
child 249, familySecrets: string
child 250, yr2003: string
child 251, boston: string
child 252, america: string
child 253, jumpShot: string
child 254, legMuscle: string
child 255, yuri: string
child 256, steinhauer: string
child 257, duMaurierClassic: string
child 258, year1992: string
child 259, descampe: string
child 260, belgium: string
child 261, jane: string
child 262, kiki: string
child 263, library: string
child 264, computerScienceDepartment: string
child 265, university: string
child 266, databaseCourse: string
child 267, professorDavid: string
child 268, lab: string
child 269, george: string
child 270, heinrichSchmidt: string
child 271, prussianStateParliament: string
child 272, naziReichstag: string
child 273, ailtonSilva: string
child 274, ailton: string
child 275, year1995: string
child 276, braga: string
child 277, nautico: string
child 278, fluminense: string
id: string
NLI_requires_more_info: string
label_old: string
ambiguity_commentary: string
amniguity_explanation: string
label_z3: string
note: string
FOL_sentence_old: string
label_new: string
label_mismatch_explanation: string
corrected: string
label: string
FOL_sentence: string
correction_explanation: string
ambiguity: bool
ambiguity_explanation: string
corerection_explanation: string
label_old_z3: string
correction: string
NL_sentence: string
to
{'id': Value('string'), 'NL_sentence': Value('string'), 'FOL_sentence': Value('string'), 'corrected': Value('string'), 'ambiguity': Value('bool'), 'ambiguity_explanation': Value('string'), 'correction_explanation': Value('string'), 'FOL_sentence_old': Value('string'), 'label': Value('string'), 'label_old': Value('string'), 'label_old_z3': Value('string'), 'label_z3': Value('string'), 'note': Value('string'), 'correction': Value('string'), 'label_new': Value('string'), 'NLI_requires_more_info': Value('string'), 'ambiguity_commentary': Value('string'), 'corerection_explanation': Value('string'), 'label_mismatch_explanation': Value('string'), 'amniguity_explanation': Value('string')}
because column names don't match
The above exception was the direct cause of the following exception:
Traceback (most recent call last):
File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 1348, in compute_config_parquet_and_info_response
parquet_operations = convert_to_parquet(builder)
^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 980, in convert_to_parquet
builder.download_and_prepare(
File "/usr/local/lib/python3.12/site-packages/datasets/builder.py", line 890, in download_and_prepare
self._download_and_prepare(
File "/usr/local/lib/python3.12/site-packages/datasets/builder.py", line 951, in _download_and_prepare
self._prepare_split(split_generator, **prepare_split_kwargs)
File "/usr/local/lib/python3.12/site-packages/datasets/builder.py", line 1683, in _prepare_split
for job_id, done, content in self._prepare_split_single(
^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/usr/local/lib/python3.12/site-packages/datasets/builder.py", line 1869, in _prepare_split_single
raise DatasetGenerationError("An error occurred while generating the dataset") from e
datasets.exceptions.DatasetGenerationError: An error occurred while generating the datasetNeed help to make the dataset viewer work? Make sure to review how to configure the dataset viewer, and open a discussion for direct support.
id string | NL_sentence string | FOL_sentence string | corrected string | ambiguity bool | ambiguity_explanation string | correction_explanation string | FOL_sentence_old string | label string | label_old string | label_old_z3 string | label_z3 string | note string | correction string | label_new string | NLI_requires_more_info string | ambiguity_commentary string | corerection_explanation string | label_mismatch_explanation string | amniguity_explanation string |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
story_380 | People in this club who perform in school talent shows often attend and are very engaged with school events. People in this club either perform in school talent shows often or are inactive and disinterested community members. People in this club who chaperone high school dances are not students who attend the school. A... | ∀x (InThisClub(x) ∧ PerformOftenIn(x, schoolTalentShow) → Attend(x, schoolEvent) ∧ VeryEngagedWith(x, schoolEvent)) ∧ ∀x (InThisClub(x) → PerformOftenIn(x, schoolTalentShow) ⊕ (InActive(x) ∧ Disinterested(x) ∧ MemberOf(x, community))) ∧ ∀x (InThisClub(x) ∧ Chaperone(x, highSchoolDance) → ¬(Student(x) ∧ AttendSchool(x))... | yes | true | either_or | 1. Spelling: Corrected 'Studen' to 'Student' and 'bonne' to 'bonnie'. 2. Linkage: 'highSchoolDances' changed to 'highSchoolDance' in Premise 4. 3. Missing Parenthesis & Operators: Fixed the missing opening parenthesis for the implication in Premise 5. Changed 'YoungChildren' to 'YoungChild' and XOR '⊕' to inclusive OR ... | ∀x (InThisClub(x) ∧ PerformOftenIn(x, schoolTalentShow) → Attend(x, schoolEvent) ∧ VeryEngagedWith(x, schoolEvent))
∀x (InThisClub(x) → PerformOftenIn(x, schoolTalentShow) ⊕ (InActive(x) ∧ Disinterested(x) ∧ MemberOf(x, community)))
∀x (InThisClub(x) ∧ Chaperone(x, highSchoolDance) → ¬(Studen(x) ∧ AttendSchool(x)))
∀x ... | null | null | null | null | null | null | null | null | null | null | null | null |
concl_380_1 | Bonnie performs in school talent shows often. | PerformOftenIn(bonnie, schoolTalentShow) | yes | null | null | 1. Predicate Match: Corrected 'Perform' to 'PerformOftenIn' to match the premises. 2. Removed Extraneous Conjunction: The original included 'InThisClub(bonnie)' which is not stated in the conclusion NL. The conclusion only asserts the performance. | InThisClub(bonnie) ∧ (Perform(bonnie, schoolTalentShow)) | Uncertain | Uncertain | not_parsable | Uncertain | null | null | null | null | null | null | null | null |
concl_380_2 | If Bonnie is either both a young child or teenager who wishes to further her academic career and educational opportunities and chaperones high school dances or neither is a young child nor teenager who wishes to further her academic career and educational opportunities, then Bonnie is either a student who attends the s... | (((YoungChild(bonnie) ∨ Teenager(bonnie)) ∧ WishToFurther(bonnie, academicCareer) ∧ WishToFurther(bonnie, educationalOpportunity) ∧ Chaperone(bonnie, highSchoolDance)) ⊕ (¬(YoungChild(bonnie) ∨ Teenager(bonnie)) ∧ ¬WishToFurther(bonnie, academicCareer) ∧ ¬WishToFurther(bonnie, educationalOpportunity))) → ((Student(bonn... | yes | true | either_or | 1. Syntax & Unbalanced Parentheses: Completely rebuilt the formula to fix severe syntax errors and unmatched parentheses. 2. Variable Scope: Replaced the unbound 'x' with 'bonnie' in 'Student'. 3. Predicate Consistency: Corrected 'Studen' to 'Student' and 'YoungChildren' to 'YoungChild'. 4. Consequent Match: Rewrote th... | ¬((YoungChildren(bonnie) ⊕ Teenager(bonnie)) ∧ WishToFurther(bonnie, academicCareer)) ⊕ Chaperone(bonnie, highSchoolDance)) → (Studen(x) ∧ AttendSchool(x)) ⊕ (YoungChildren(bonnie) ⊕ Teenager(bonnie)) ∧ WishToFurther(bonnie, academicCareer)) | True | True | not_parsable | True | null | null | null | null | null | null | null | null |
concl_380_3 | If Bonnie either chaperones high school dances or, if she does not, she performs in school talent shows often, then Bonnie is both a young child or teenager who wishes to further her academic career and educational opportunities and an inactive and disinterested member of the community. | (Chaperone(bonnie, highSchoolDance) ⊕ PerformOftenIn(bonnie, schoolTalentShow)) → ((YoungChild(bonnie) ∨ Teenager(bonnie)) ∧ WishToFurther(bonnie, academicCareer) ∧ WishToFurther(bonnie, educationalOpportunity) ∧ InActive(bonnie) ∧ Disinterested(bonnie) ∧ MemberOf(bonnie, community)) | yes | true | either_or | Predicate Match: Corrected 'Perform' to 'PerformOftenIn' to properly link with the premises. Missing Entities: Added 'WishToFurther(bonnie, educationalOpportunity)' to strictly align with the NL. | (Chaperone(bonnie, highSchoolDance) ⊕ Perform(bonnie, schoolTalentShow)) → (YoungChildren(bonnie) ⊕ Teenager(bonnie)) ∧ WishToFurther(bonnie, academicCareer)) ∧ (InActive(bonnie) ∧ Disinterested(bonnie) ∧ MemberOf(bonnie, community)) | False | False | not_parsable | False | null | null | null | null | null | null | null | null |
story_426 | All employees who schedule a meeting with their customers will go to the company building today. Everyone who has lunch in the company building schedules meetings with their customers. Employees have lunch either in the company building or at home. If an employee has lunch at home, they are working remotely from home. ... | ∀x ((Employee(x) ∧ Schedule(x, meeting, customers)) → AppearIn(x, company)) ∧ ∀x (HasLunch(x, company) → Schedule(x, meeting, customers)) ∧ ∀x (Employee(x) → (HasLunch(x, company) ⊕ HasLunch(x, home))) ∧ ∀x ((Employee(x) ∧ HasLunch(x, home)) → Work(x, home)) ∧ ∀x ((Employee(x) ∧ (¬In(x, homeCountry))) → Work(x, home)) ... | yes | true | either_or | 1. 'Everyone who has lunch in the company' is relativized to 'everyone that is an employee', but this restriction is not present in NL | ∀x ((Employee(x) ∧ Schedule(x, meeting, customers)) → AppearIn(x, company))
∀x ((Employee(x) ∧ HasLunch(x, company)) → Schedule(x, meeting, customers))
∀x (Employee(x) → (HasLunch(x, company) ⊕ HasLunch(x, home)))
∀x ((Employee(x) ∧ HasLunch(x, home)) → Work(x, home))
∀x ((Employee(x) ∧ (¬In(x, homeCountry))) → Work(x,... | null | null | null | null | null | null | null | null | null | null | null | null |
concl_426_4 | James has lunch in the company. | HasLunch(james, company) | no | null | null | null | HasLunch(james, company) | Uncertain | Uncertain | Uncertain | Uncertain | null | null | null | null | null | null | null | null |
concl_426_5 | James does not have lunch in the company. | ¬HasLunch(james, company) | no | null | null | null | ¬HasLunch(james, company) | Uncertain | Uncertain | Uncertain | Uncertain | null | null | null | null | null | null | null | null |
concl_426_6 | If James is either a manager or in other countries, then James does not either have lunch at home or work remotely from home. If James either has lunch at home or works remotely from home, then he is neither a manager nor does he work in other countries. | ((Manager(james) ∨ ¬In(james, homeCountry)) → ¬(HasLunch(james, home) ∨ Work(james, home))) ∧ ((HasLunch(james, home) ∨ Work(james, home)) → ¬(Manager(james) ∨ ¬In(james, homeCountry))) | yes | true | either_or | Translation Failure: The original FOL 'Manager(james) → ¬Work(james, home)' completely ignored the vast majority of the NL sentence. The NL contains two complex conditionals that act as contrapositives involving 'in other countries' and 'lunch at home'. The FOL has been rewritten to exhaustively translate the English s... | Manager(james) → ¬Work(james, home) | Uncertain | True | True | Uncertain | null | null | null | null | null | null | null | null |
story_198 | When the Monkeypox virus occurs in a being, it may get Monkeypox. Monkeypox virus can occur in certain animals. Humans are mammals. Mammals are animals. Symptoms of Monkeypox include fever, headache, muscle pains, and tiredness. People feel tired when they get the flu. | ∃x (OccurIn(monkeypoxVirus, x) ∧ Get(x, monkeypoxVirus)) ∧ ∃x (Animal(x) ∧ OccurIn(monkeypoxVirus, x)) ∧ ∀x (Human(x) → Mammal(x)) ∧ ∀x (Mammal(x) → Animal(x)) ∧ ∀x ((Fever(x) ∨ Headache(x) ∨ MusclePain(x) ∨ Tiredness(x)) → SymptomOf(x, monkeypoxVirus)) ∧ ∀x (Human(x) ∧ Get(x, flu) → Feel(x, tired)) | yes | null | null | 1. Translation Failure (Premise 5): The original FOL weakly asserted via an existential quantifier ('∃x') that there is at least one symptom that is one of those conditions. The NL 'Symptoms ... include ...' requires a universal implication to denote that all instances of these conditions are symptoms. Corrected to '∀x... | ∃x (OccurIn(monkeypoxVirus, x) ∧ Get(x, monkeypoxVirus))
∃x (Animal(x) ∧ OccurIn(monkeypoxVirus, x))
∀x (Human(x) → Mammal(x))
∀x (Mammal(x) → Animal(x))
∃x (SymptonOf(x, monkeypoxVirus) ∧ (Fever(x) ∨ Headache(x) ∨ MusclePain(x) ∨ Tired(x)))
∀x (Human(x) ∧ Get(x, flu) → Feel(x, tired)) | null | null | null | null | null | null | null | null | null | null | null | null |
concl_198_7 | There is an animal. | ∃x (Animal(x)) | no | null | null | null | ∃x (Animal(x)) | True | True | True | True | null | null | null | null | null | null | null | null |
concl_198_8 | No one gets the flu. | ∀x (Human(x) → ¬Get(x, flu)) | no | null | null | There is no referement to humans (in the story it is talked about animals also), but usually 'no one' refer to human beings, so the original formalization can be considered acceptable | ∀x (Human(x) → ¬Get(x, flu)) | Uncertain | Uncertain | Uncertain | Uncertain | null | null | null | null | null | null | null | null |
concl_198_9 | Symptoms of Monkeypox include coughing. | ∃x (SymptomOf(x, monkeypoxVirus) ∧ Coughing(x)) | yes | null | null | 1. Typo: Corrected 'SymptonOf' to 'SymptomOf'. | ∃x (SymptonOf(x, monkeypoxVirus) ∧ Coughing(x)) | Uncertain | Uncertain | Uncertain | Uncertain | null | null | null | null | null | null | null | null |
story_0 | There are six types of wild turkeys: Eastern wild turkey, Osceola wild turkey, Gould's wild turkey, Merriam's wild turkey, Rio Grande wild turkey, and Ocellated wild turkey. Tom is not an Eastern wild turkey. Tom is not an Osceola wild turkey. Tom is not a Gould's wild turkey. Tom is neither a Merriam's wild turkey nor... | ∀x (WildTurkey(x) ↔ (EasternWildTurkey(x) ∨ OsceolaWildTurkey(x) ∨ GouldsWildTurkey(x) ∨ MerriamsWildTurkey(x) ∨ RiograndeWildTurkey(x) ∨ OcellatedWildTurkey(x))) ∧ ¬(EasternWildTurkey(tom)) ∧ ¬(OsceolaWildTurkey(tom)) ∧ ¬(GouldsWildTurkey(tom)) ∧ ¬(MerriamsWildTurkey(tom) ∨ RiograndeWildTurkey(tom)) ∧ WildTurkey(tom) | yes | true | option_partition | Now inserted a bi-implication instead of a simple implication, since if x is an eastern wild turkey, then it is also a wild turkey. | ∀x (WildTurkey(x) → (EasternWildTurkey(x) ∨ OsceolaWildTurkey(x) ∨ GouldsWildTurkey(x) ∨ MerriamsWildTurkey(x) ∨ RiograndeWildTurkey(x) ∨ OcellatedWildTurkey(x)))
¬(EasternWildTurkey(tom))
¬(OsceolaWildTurkey(tom))
¬(GouldsWildTurkey(tom))
¬(MerriamsWildTurkey(tom) ∨ RiograndeWildTurkey(tom))
WildTurkey(tom) | null | null | null | null | null | null | null | null | null | null | null | null |
concl_0_10 | Tom is an Ocellated wild turkey. | OcellatedWildTurkey(tom) | no | null | null | null | OcellatedWildTurkey(tom) | True | True | True | True | null | null | null | null | null | null | null | null |
concl_0_11 | Tom is an Eastern wild turkey. | EasternWildTurkey(tom) | no | null | null | null | EasternWildTurkey(tom) | False | False | False | False | null | null | null | null | null | null | null | null |
concl_0_12 | Joey is a wild turkey. | WildTurkey(joey) | no | null | null | null | WildTurkey(joey) | Uncertain | Uncertain | Uncertain | Uncertain | null | null | null | null | null | null | null | null |
story_20 | A Japanese game company created the game the Legend of Zelda. All games on the Top 10 list are made by Japanese game companies. If a game sells more than one million copies, then it will be included in the Top 10 list. The Legend of Zelda sold more than one million copies. | Game(theLegendofZelda) ∧ ∃x (Japanese(x) ∧ VideoGameCompany(x) ∧ Created(x, theLegendofZelda)) ∧ ∀x ∀y ((Game(x) ∧ InTop10(x) ∧ Created(y,x)) → (Japanese(y) ∧ VideoGameCompany(y))) ∧ ∀x ((Game(x) ∧ ∃y(GreaterThan(y, oneMillion) ∧ CopiesSold(x, y))) → InTop10(x)) ∧ ∃y(GreaterThan(y, oneMillion) ∧ CopiesSold(theLegendofZ... | yes | null | null | 1. Translation Failure (Premise 2): The NL says 'Japanese game companies', but the old FOL only asserted 'Japanese(y)'. Corrected the consequent to '(Japanese(y) ∧ VideoGameCompany(y))'. 2. Syntax Error (Premise 3): Removed an unmatched closing parenthesis. 3. Broken Predicate Link (Premise 2 & 3): Standardized 'Top10'... | Game(theLegendofZelda) ∧ ∃x (Japanese(x) ∧ VideoGameCompany(x) ∧ Created(x, theLegendofZelda))
∀x ∀y ((Game(x) ∧ InTop10(x) ∧ Created(y,x)) → Japanese(y))
∀x ((Game(x) ∧ ∃y(GreaterThan(y, oneMillion) ∧ CopiesSold(x, y))) → Top10(x)))
∃y(GreaterThan(y, oneMillion) ∧ CopiesSold(theLegendofZelda,y)) | null | null | null | null | null | null | null | null | null | null | null | null |
concl_20_13 | The Legend of Zelda is on the Top 10 list. | InTop10(theLegendofZelda) | yes | null | null | Standardized the predicate 'Top10' to 'InTop10' to correctly link with the adjusted premises. | Top10(theLegendofZelda) | True | True | not_parsable | True | null | null | null | null | null | null | null | null |
concl_20_14 | FIFA 22 is made by a Japanese video game company. | ∃x(Created(x, fifa22) ∧ Japanese(x) ∧ VideoGameCompany(x)) | no | null | null | null | ∃x(Created(x, fifa22) ∧ Japanese(x) ∧ VideoGameCompany(x)) | Uncertain | Uncertain | not_parsable | Uncertain | null | null | null | null | null | null | null | null |
concl_20_15 | The Legend of Zelda is not on the Top 10 list. | ¬InTop10(theLegendofZelda) | yes | null | null | Standardized the predicate 'Top10' to 'InTop10' to correctly link with the adjusted premises. | ¬Top10(theLegendofZelda) | False | False | not_parsable | False | null | null | null | null | null | null | null | null |
story_282 | All squares are four-sided. All four-sided things are shapes. | ∀x (Square(x) → FourSided(x)) ∧ ∀x (FourSided(x) → Shape(x)) | no | null | null | null | ∀x (Square(x) → FourSided(x))
∀x (FourSided(x) → Shape(x)) | null | null | null | null | null | null | null | null | null | null | null | null |
concl_282_16 | All squares are shapes. | ∀x (Square(x) → Shape(x)) | no | null | null | null | ∀x (Square(x) → Shape(x)) | True | True | True | True | null | null | null | null | null | null | null | null |
story_471 | All rabbits that can be spotted near the campus are cute. Some turtles can be spotted near the campus. The only animals that can be spotted near the campus are rabbits and squirrels. If something is skittish, then it is not calm. All the squirrels that can be spotted near the campus are skittish. Rockie can be spotted ... | ∀x (Rabbit(x) ∧ CanBeSpottedNear(x, campus) → Cute(x)) ∧ ∃x (Turtle(x) ∧ CanBeSpottedNear(x, campus)) ∧ ∀x (CanBeSpottedNear(x, campus) → (Rabbit(x) ∨ Squirrel(x))) ∧ ∀x (Skittish(x) → ¬Calm(x)) ∧ ∀x (Squirrel(x) ∧ CanBeSpottedNear(x, campus) → Skittish(x)) ∧ CanBeSpottedNear(rockie, campus) ∧ Calm(rockie) | yes | true | some_plural | 1. Translation Failure (Premise 3): Corrected the exclusive OR '⊕' to an inclusive OR '∨'. The NL states 'are rabbits and squirrels', which translates logically to the union of those two sets, not strictly an XOR relationship. 2. Silent Edits Reverted (Premises 1, 5, 6): Removed hallucinated inner and outer parentheses... | ∀x (Rabbit(x) ∧ CanBeSpottedNear(x, campus) → Cute(x))
∃x (Turtle(x) ∧ CanBeSpottedNear(x, campus))
∀x (CanBeSpottedNear(x, campus) → (Rabbit(x) ⊕ Squirrel(x)))
∀x (Skittish(x) → ¬Calm(x))
∀x (Squirrel(x) ∧ CanBeSpottedNear(x, campus) → Skittish(x))
CanBeSpottedNear(rockie, campus) ∧ Calm(rockie) | null | null | null | null | null | null | null | null | null | null | null | null |
concl_471_17 | Rockie is a turtle. | Turtle(rockie) | no | null | null | null | Turtle(rockie) | Uncertain | Uncertain | Uncertain | Uncertain | null | null | null | null | null | null | null | null |
concl_471_18 | Rockie is not a turtle. | ¬Turtle(rockie) | no | null | null | null | ¬Turtle(rockie) | Uncertain | Uncertain | Uncertain | Uncertain | null | null | null | null | null | null | null | null |
concl_471_19 | Rockie is a turtle or cute. | Turtle(rockie) ∨ Cute(rockie) | no | null | null | null | Turtle(rockie) ∨ Cute(rockie) | True | True | True | True | null | null | null | null | null | null | null | null |
concl_471_20 | If Rockie is not both a turtle and a squirrel, then Rockie is either cute or skittish. | ¬(Turtle(rockie) ∧ Squirrel(rockie)) → (Cute(rockie) ⊕ Skittish(rockie)) | yes | true | either_or | Added parentheses because of operator precedences | ¬(Turtle(rockie) ∧ Squirrel(rockie)) → Cute(rockie) ⊕ Skittish(rockie) | True | True | True | True | null | null | null | null | null | null | null | null |
concl_471_21 | If Rockie is cute and calm, then Rockie is a skittish turtle. | (Cute(rockie) ∧ Calm(rockie)) → (Turtle(rockie) ∧ Skittish(rockie)) | no | null | null | Added parentheses (even if not necessary): it is not considered a correction. | Cute(rockie) ∧ Calm(rockie) → Turtle(rockie) ∧ Skittish(rockie) | False | False | False | False | null | null | null | null | null | null | null | null |
story_184 | "Stranger Things" is a popular Netflix show. If a Netflix show is popular, Karen will binge-watch it. If and only if Karen binge-watches a Netflix show, she will download it. Karen does not download "Black Mirror". "Black Mirror" is a Netflix show. If Karen binge-watches a Netflix show, she will share it with Lisa. | NetflixShow(strangerThings) ∧ Popular(strangerThings) ∧ ∀x ((NetflixShow(x) ∧ Popular(x)) → BingeWatch(karen, x)) ∧ ∀x (NetflixShow(x) → (BingeWatch(karen, x) ↔ Download(karen, x))) ∧ ¬Download(karen, blackMirror) ∧ NetflixShow(blackMirror) ∧ ∀x ((NetflixShow(x) ∧ BingeWatch(karen, x)) → ShareWith(karen, x, lisa)) | yes | null | null | Karen may download things that are not Netflix shows, but the original FOL incorrectly restricted the biconditional to only Netflix shows. The NL states 'If and only if Karen binge-watches a Netflix show, she will download it', which means the biconditional should be between 'BingeWatch(karen, x)' and 'Download(karen, ... | NetflixShow(strangerThings) ∧ Popular(strangerThings)
∀x ((NetflixShow(x) ∧ Popular(x)) → BingeWatch(karen, x))
∀x ((NetflixShow(x) ∧ BingeWatch(karen, x)) ↔ Download(karen, x))
¬Download(karen, blackMirror)
NetflixShow(blackMirror)
∀x ((NetflixShow(x) ∧ BingeWatch(karen, x)) → ShareWith(karen, x, lisa)) | null | null | null | null | null | null | null | null | null | null | null | null |
concl_184_22 | Karen will share "Stranger Things" with Lisa. | ShareWith(karen, strangerThings, lisa) | no | null | null | null | ShareWith(karen, strangerThings, lisa) | True | True | True | True | null | null | null | null | null | null | null | null |
concl_184_23 | "Black Mirror" is popular. | Popular(blackMirror) | no | null | null | null | Popular(blackMirror) | False | False | False | False | null | null | null | null | null | null | null | null |
concl_184_24 | Karen will share "Black Mirror" with Lisa. | ShareWith(karen, blackMirror, lisa) | no | null | null | null | ShareWith(karen, blackMirror, lisa) | Uncertain | Uncertain | Uncertain | Uncertain | null | null | null | null | null | null | null | null |
story_232 | Beijing is the capital of the People's Republic of China. Beijing is the capital city of the world's most populous nation. Beijing is located in Northern China. Beijing hosted the 2008 Summer Olympics and 2008 Summer Paralympics Games. Beijing has hosted the Summer and Winter Olympics and the Summer and Winter Paralymp... | CapitalOf(beijing, peoplesRepublicOfChina) ∧ ∃x (WorldsMostPopulousNation(x) ∧ CapitalOf(beijing, x)) ∧ LocatedIn(beijing, northernChina) ∧ Hosted(beijing, summerOlympics2008) ∧ Hosted(beijing, summerParalympicGames2008) ∧ Hosted(beijing, summerOlympics) ∧ Hosted(beijing, winterOlympics) ∧ Hosted(beijing, summerParalym... | yes | null | null | 1. Translation Failure (Premise 2): The original '∃x (CapitalOf(beijing, x) → ...)' is a weak existential implication that evaluates to true if there is literally anything Beijing is NOT the capital of. Corrected to an existential conjunction '∃x (WorldsMostPopulousNation(x) ∧ CapitalOf(beijing, x))' to accurately capt... | CapitalOf(beijing, peoplesRepublicOfChina)
∃x (CapitalOf(beijing, x) → WorldsMostPopulousNation(x))
LocatedIn(beijing, northernChina)
Hosted(beijing, 2008SummerOlympics) ∧ Hosted(beijing, 2008SummerParalympicGames)
Hosted(beijing, summerOlympics) ∧ Hosted(beijing, winterOlympics) ∧ Hosted(beijing, summerParalympicGames... | null | null | null | null | null | null | null | null | null | null | null | null |
concl_232_25 | Beijing hosted both the 2008 Summer Olympics and the Winter Olympics. | Hosted(beijing, summerOlympics2008) ∧ Hosted(beijing, winterOlympics) | yes | null | null | Translation Failure: The old FOL used 'summerOlympics' which refers to the generic games from Premise 5, but the NL specifically calls out the '2008 Summer Olympics'. Updated to use 'summerOlympics2008' to accurately reflect the text and correctly link to Premise 4. | Hosted(beijing, summerOlympics) ∧ Hosted(beijing, winterOlympics) | True | True | True | True | null | null | null | null | null | null | null | null |
concl_232_26 | Beijing is located in southern China. | LocatedIn(beijing, southernChina) | no | null | null | null | LocatedIn(beijing, southernChina) | Uncertain | Uncertain | Uncertain | Uncertain | null | null | null | null | null | null | null | null |
concl_232_27 | Beijing is the second largest Chinese city. | SecondLargestChineseCity(beijing) | no | null | null | null | SecondLargestChineseCity(beijing) | Uncertain | Uncertain | Uncertain | Uncertain | null | null | null | null | null | null | null | null |
story_452 | All aliens are extraterrestrials. If someone is from Mars, then they are an alien. No extraterrestrials are human. All highly intelligent beings from Earth are humans. Marvin is a highly intelligent being. Marvin is either from Earth and from Mars, or he is from neither. If Marvin is not from Earth, then Marvin is an e... | ∀x (Alien(x) → Extraterrestrial(x)) ∧ ∀x (From(x, mars) → Alien(x)) ∧ ∀x (Extraterrestrial(x) → ¬Human(x)) ∧ ∀x (HighlyIntelligentBeing(x) ∧ From(x, earth) → Human(x)) ∧ HighlyIntelligentBeing(marvin) ∧ ¬(From(marvin, earth) ⊕ From(marvin, mars)) ∧ (¬From(marvin, earth) → Extraterrestrial(marvin)) | no | true | either_or | No semantic corrections required. The original FOL accurately translated the NL sentences. The negated XOR '¬(A ⊕ B)' perfectly captures the 'both or neither' phrasing of the NL. Minor additions of grouping parentheses for readability do not constitute a formal correction. | ∀x (Alien(x) → Extraterrestrial(x))
∀x (From(x, mars) → Alien(x))
∀x (Extraterrestrial(x) → ¬Human(x))
∀x (HighlyIntelligentBeing(x) ∧ From(x, earth) → Human(x))
HighlyIntelligentBeing(marvin)
¬(From(marvin, earth) ⊕ From(marvin, mars))
¬From(marvin, earth) → Extraterrestrial(marvin) | null | null | null | null | null | null | null | null | null | null | null | null |
concl_452_28 | Marvin is an alien. | Alien(marvin) | no | null | null | null | Alien(marvin) | Uncertain | Uncertain | Uncertain | Uncertain | null | null | null | null | null | null | null | null |
concl_452_29 | Marvin is neither a human nor from Mars. | ¬Human(marvin) ∧ ¬From(marvin, mars) | no | null | null | null | ¬Human(marvin) ∧ ¬From(marvin, mars) | True | True | True | True | null | null | null | null | null | null | null | null |
concl_452_30 | If Marvin is not from Mars, then Marvin is a human. | ¬From(marvin, mars) → Human(marvin) | no | null | null | null | ¬From(marvin, mars) → Human(marvin) | False | False | False | False | In the only consistent case (Case B), ¬From(marvin, mars) is true but Human(marvin) is false, making the implication false. Label False is correct. | null | null | null | null | null | null | null |
story_340 | Everyone at the mixer is a Grand Slam champion or an Oscar-nominated actor. Every Grand Slam champion at the mixer is a professional tennis player. All Oscar-nominated actors at the mixer are celebrities. All professional tennis players at the mixer are athletes. If a person at the mixer is a celebrity, then they are w... | ∀x (At(x, mixer) → (GrandSlamChampion(x) ∨ (OscarNominated(x) ∧ Actor(x)))) ∧ ∀x (At(x, mixer) → (GrandSlamChampion(x) → (Professional(x) ∧ TennisPlayer(x)))) ∧ ∀x (At(x, mixer) → ((OscarNominated(x) ∧ Actor(x)) → Celebrity(x))) ∧ ∀x ((At(x, mixer) ∧ Professional(x) ∧ TennisPlayer(x)) → Athlete(x)) ∧ ∀x ((At(x, mixer) ... | yes | null | null | Corrections applied: (1) Premises 2 and 3: The original FOL statements contained fatal syntax errors (missing closing parentheses) and a major semantic error (using a conjunction '∧' instead of an implication '→' for a universal claim, which asserted that everyone at the mixer actually *is* a champion/actor rather than... | ∀x (At(x, mixer) → (GrandSlam(x) ∧ Champion(x)) ∨ (OscarNominated(x) ∧ Actor(x)))
∀x (At(x, mixer) ∧ (GrandSlam(x) ∧ Champion(x) → Professional(x) ∧ TennisPlayer(x))
∀x (At(x, mixer) ∧ (OscarNominated(x) ∧ Actor(x) → Celebrity(x))
∀x (At(x, mixer) ∧ Professional(x) ∧ TennisPlayer(x) → Athlete(x))
∀x (At(x, mixer) ∧ Cel... | null | null | null | null | null | null | null | null | null | null | null | null |
concl_340_31 | Djokovic is a Grand Slam champion. | GrandSlamChampion(djokovic) | yes | null | null | Note: label_31 was missing from the original input (label_32 was written twice); label inferred from context as 'Uncertain' based on the value appearing in the field wrongly assigned to conclusion_31. Unified the predicate symbols as written in story_340. | GrandSlam(djokovic) ∧ Champion(djokovic) | Uncertain | Uncertain | not_parsable | Uncertain | null | null | null | null | null | null | null | null |
concl_340_32 | Djokovic lives in a tax haven. | ∃x (TaxHaven(x) ∧ LiveIn(djokovic, x)) | yes | null | null | TaxHaven is a predicate now | LiveIn(djokovic, taxHaven) | True | True | not_parsable | True | null | null | null | null | null | null | null | null |
concl_340_33 | Djokovic does not live in a tax haven. | ¬ (∃x (TaxHaven(x) ∧ LiveIn(djokovic, x))) | yes | null | null | null | ¬LiveIn(djokovic, taxHaven) | False | False | not_parsable | False | null | TaxHaven is a predicate now | null | null | null | null | null | null |
story_96 | Diamond Mine is a professional wrestling stable formed in WWE. Roderick Strong leads Diamond Mine. Diamond Mine includes the Creed Brothers and Ivy Nile. Imperium has a feud with Diamond Mine. | ProfessionalWrestlingStable(diamondMine) ∧ In(diamondMine, wWE) ∧ Leads(roderickStrong, diamondMine) ∧ Includes(diamondMine, creedBrothers) ∧ Includes(diamondMine, ivyNile) ∧ Feuds(imperium, diamondMine) | no | null | null | null | ProfessionalWrestlingStable(diamondMine) ∧ In(diamondMine, wWE)
Leads(roderickStrong, diamondMine)
Includes(diamondMine, creedBrothers) ∧ Includes(diamondMine, ivyNile)
Feuds(imperium, diamondMine) | null | null | null | null | null | null | null | null | null | null | null | null |
concl_96_34 | Roderick Strong leads a professional wrestling stable. | ∃x (Leads(roderickStrong, x) ∧ ProfessionalWrestlingStable(x)) | yes | null | null | The constant 'roderickstrong' was written in all lowercase in the original FOL, inconsistently with the camelCase convention used in the premises ('roderickStrong'). Normalised to 'roderickStrong' for consistency. | ∃x (Leads(roderickstrong, x) ∧ ProfessionalWrestlingStable(x)) | True | True | Uncertain | True | null | null | null | null | null | null | null | null |
concl_96_35 | Roderick Strong leads the Creed Brothers. | Leads(roderickStrong, creedBrothers) | yes | null | null | Same casing issue as conclusion 34: 'roderickstrong' → 'roderickStrong' and 'creedbrothers' → 'creedBrothers', to align with camelCase convention used in the premises. | Leads(roderickstrong, creedbrothers) | Uncertain | Uncertain | Uncertain | Uncertain | null | null | null | null | null | null | null | null |
concl_96_36 | Imperium doesn't have a feud with a professional wrestling stable that includes Ivy Nile. | ∀x ((ProfessionalWrestlingStable(x) ∧ Includes(x, ivyNile)) → ¬Feuds(imperium, x)) | yes | null | null | Casing issue: 'ivynile' → 'ivyNile' to align with camelCase convention used in the premises. | ∀x ((ProfessionalWrestlingStable(x) ∧ Includes(x, ivynile)) → ¬Feuds(imperium, x)) | False | False | Uncertain | False | null | null | null | null | null | null | null | null |
story_219 | Symphony No. 9 is a music piece. Composers write music pieces. Beethoven wrote Symphony No. 9. Vienna Music Society premiered Symphony No. 9. Vienna Music Society is an orchestra. Beethoven leads the Vienna Music Society. Orchestras are led by conductors. | MusicPiece(symphony9) ∧ ∀x(Composer(x) → ∃y(MusicPiece(y) ∧ Write(x, y))) ∧ Write(beethoven, symphony9) ∧ Premiered(viennaMusicSociety, symphony9) ∧ Orchestra(viennaMusicSociety) ∧ Lead(beethoven, viennaMusicSociety) ∧ ∀x (Orchestra(x) → ∃y (Conductor(y) ∧ Lead(y, x))) | yes | true | Composers write music pieces can be interpreted as: it can mean that all the composers write some music pieces, that only composers write music pieces, .... Here it is translated in the first way | Corrections applied: (1) Premise 3: The original 'Writtenby(symphony9, beethoven)' uses an inconsistent predicate. To properly resolve against Premise 2's 'Write(y, x)', it must be rewritten as 'Write(beethoven, symphony9)'. (2) Premise 7: The original FOL contained a critical scoping error '... (∃y Conductor(y) ∧ Lead... | MusicPiece(symphony9)
∀x (MusicPiece(x) → ∃y (Composer(y) ∧ Write(y, x)))
Writtenby(symphony9, beethoven)
Premiered(viennaMusicSociety, symphony9)
Orchestra(viennaMusicSociety)
Lead(beethoven, viennaMusicSociety)
∀x (Orchestra(x) → (∃y Conductor(y) ∧ Lead(y, x))) | null | null | null | null | null | null | null | null | null | null | null | null |
concl_219_37 | Beethoven is a composer. | Composer(beethoven) | no | null | null | Label correction: The original label 'True' is invalid in strict formal logic. While Premise 2 states every music piece has some composer who wrote it, and Premise 3 states Beethoven wrote it, there is no rule stating that ONLY composers write music pieces or that a piece has a unique writer. Thus, 'Composer(beethoven)... | Composer(beethoven) | null | True | Uncertain | Uncertain | null | null | Uncertain | null | null | null | null | null |
concl_219_38 | Some orchestras premiered music pieces. | ∃x ∃y (Orchestra(x) ∧ MusicPiece(y) ∧ Premiered(x, y)) | no | true | some_plural | null | ∃x ∃y (Orchestra(x) ∧ MusicPiece(y) ∧ Premiered(x, y)) | True | True | True | True | null | null | null | null | null | null | null | null |
concl_219_39 | Beethoven is not a conductor. | ¬Conductor(beethoven) | no | null | null | Label correction: The original label 'False' implies we can prove Beethoven IS a conductor. However, just because he leads the orchestra (P6) and a conductor leads the orchestra (P7), without an equality axiom or a rule stating ONLY conductors lead orchestras, we cannot definitively prove he is a conductor, nor can we ... | ¬Conductor(beethoven) | null | False | Uncertain | Uncertain | null | null | Uncertain | null | null | null | null | null |
story_350 | All of Zaha Hadid's design styles that Max adores have interesting geometries. No brutalist buildings that Max adores have interesting geometries. Every style that Max adores is either Zaha Hadid's design style or Kelly Wearstler's design style. All of Kelly Wearstler's design styles that Max adores are evocative. All ... | ∀x (Adore(max, x) ∧ ZahaHadid(x) ∧ DesignStyle(x) → InterestingGeometry(x)) ∧ ∀x (Adore(max, x) ∧ BrutalistBuilding(x) → ¬InterestingGeometry(x)) ∧ ∀x (Adore(max, x) → ((ZahaHadid(x) ∧ DesignStyle(x)) ⊕ (KellyWearstler(x) ∧ DesignStyle(x)))) ∧ ∀x (Adore(max, x) ∧ KellyWearstler(x) ∧ DesignStyle(x) → Evocative(x)) ∧ ∀x ... | yes | true | either_or | Two corrections made: (1) Premise 3: unclosed parenthesis in the original fixed. (2) Premise 6: the original uses '∃x (Adore(max, x) ∧ Design(x) ∧ ByMax(x) ∧ InterestingGeometry(x) → BrutalistBuilding(x) ∧ Evocative(x))'. This is a well-known FOL scoping pitfall: '∃x (P → Q)' is not the intended reading for a condition... | ∀x (Adore(max, x) ∧ ZahaHadid(x) ∧ DesignStyle(x) → InterestingGeometry(x))
∀x (Adore(max, x) ∧ BrutalistBuilding(x) → ¬InterestingGeometry(x))
∀x (Adore(max, x) → ((ZahaHadid(x) ∧ DesignStyle(x)) ⊕ (KellyWearstler(x) ∧ DesignStyle(x)))
∀x (Adore(max, x) ∧ KellyWearstler(x) ∧ DesignStyle(x) → Evocative(x))
∀x (Adore(ma... | null | null | null | null | null | null | null | null | null | null | null | null |
concl_350_40 | A design by Max is a brutalist building. | ∃x (Design(x) ∧ ByMax(x) ∧ BrutalistBuilding(x)) | no | true | existential_universal | null | ∃x (Design(x) ∧ ByMax(x) ∧ BrutalistBuilding(x)) | Uncertain | Uncertain | not_parsable | Uncertain | null | null | null | null | null | null | null | null |
concl_350_41 | A design by Max is evocative and dreamy. | ∃x (Design(x) ∧ ByMax(x) ∧ Evocative(x) ∧ Dreamy(x)) | yes | true | existential_universal | Label correction: FOR THE ORIGINAL INTERPRETATION: The original label 'True' commits an existential fallacy. The premises are exclusively universal conditionals (∀x). They establish rules about properties, but never assert that any design actually exists in the domain. Furthermore, there is no rule linking a design ByM... | ∃x (Design(x) ∧ ByMax(x) ∧ Evocative(x) ∧ Dreamy(x)) | null | True | not_parsable | Uncertain | null | null | Uncertain | null | null | null | null | null |
concl_350_42 | A design by Max is either evocative or dreamy. | ∃x (Design(x) ∧ ByMax(x) ∧ (Evocative(x) ⊕ Dreamy(x))) | yes | true | existential_universal, either_or | Label correction: The original label 'False' is logically invalid. To prove this existential statement False, the solver must prove that NO design by Max is either evocative or dreamy. Because the premises do not explicitly forbid Max from having a design that is solely evocative (e.g., via Premise 6), and because we d... | ∃x (Design(x) ∧ ByMax(x) ∧ (Evocative(x) ⊕ Dreamy(x))) | null | False | not_parsable | Uncertain | null | null | Uncertain | null | null | null | null | null |
story_385 | If someone is ranked highly by the Women's Tennis Association, then they are one of the most active players in major tennis. Everyone who lost to Iga Świątek at Roland Garros 2022 is ranked highly by the Women's Tennis Association. All female tennis players at Roland Garros 2022 lost to Iga Świątek. All tennis players ... | ∀x (RankedHighlyBy(x, womensTennisAssociation) → MostActivePlayerIn(x, majorTennis)) ∧ ∀x (LostTo(x, świątek, rolandGarros2022) → RankedHighlyBy(x, womensTennisAssociation)) ∧ ∀x ((FemaleTennisPlayer(x) ∧ At(x, rolandGarros2022)) → LostTo(x, świątek, rolandGarros2022)) ∧ ∀x ((TennisPlayer(x) ∧ At(x, rolandGarros2022)) ... | yes | true | either_or | Critical corrections applied: (1) Predicate Unification: The original FOL mixed 'Female(x) ∧ TennisPlayer(x)' with 'FemaleTennisPlayer(x)'. Standardized to 'FemaleTennisPlayer(x)' and 'MaleTennisPlayer(x)' throughout to repair the broken logical chain. (2) Translation Failure: Premise 5 incorrectly translated 'Rafael N... | ∀x (RankedHighlyBy(x, womensTennisAssociation) → MostActivePlayerIn(x, majorTennis))
∀x (LostTo(x, świątek) ∧ At(x, rolandGarros2022) → RankedHighlyBy(x, womensTennisAssociation))
∀x (FemaleTennisPlayer(x) ∧ At(x, rolandGarros2022) → LostTo(x, świątek) ∧ At(x, rolandGarros2022))
∀x (TennisPlayer(x) ∧ At(x, rolandGarr... | null | null | null | null | null | null | null | null | null | null | null | null |
concl_385_43 | Coco Gauff is among the most active major tennis players. | MostActivePlayerIn(cocoGauff, majorTennis) | no | null | null | The original NL sentence was 'Coco Gauff is among the most active Grand-Slam players.'. Most active player is mentioned only about 'major tennis' in the story and never in Grand-Slams competition. With the provided ontology is not formalizable correctly. We corrected the original NL_sentence. | MostActivePlayerIn(cocoGauff, majorTennis) | null | True | Uncertain | True | null | null | null | null | null | null | null | null |
concl_385_44 | Coco Gauff has lost to Rafael Nadal. | ∃x LostTo(cocoGauff, nadal, x) | yes | null | null | Translation correction: (1) The original FOL translated 'Rafael Nadal' as 'świątek'. Corrected to 'nadal'. (2) The original FOL inappropriately appended '∧ At(cocoGauff, rolandGarros2022)', which is a premise, not part of the conclusion's statement. Removed. (3) Used LostTo ternary. | LostTo(cocoGauff, świątek) ∧ At(cocoGauff, rolandGarros2022) | null | Uncertain | Uncertain | Uncertain | null | null | null | null | null | null | null | null |
concl_385_45 | Coco Gauff is not both a player who lost to Iga Świątek at Roland Garros 2022 and one of the most active players in major tennis. | ¬LostTo(cocoGauff, świątek, rolandGarros2022) ∨ ¬MostActivePlayerIn(cocoGauff, majorTennis) | yes | null | null | ontology_correction | ¬(LostTo(cocoGauff, świątek) ∧ At(cocoGauff, rolandGarros2022)) ∨ ¬MostActivePlayerIn(cocoGauff, majorTennis) | null | False | Uncertain | False | null | null | null | null | null | null | null | null |
story_256 | All cats are mammals. Some pets are not mammals. | ∀x (Cat(x) → Mammal(x)) ∧ ∃x (Pet(x) ∧ ¬Mammal(x)) | no | true | some_plural | null | ∀x (Cat(x) → Mammal(x))
∃x (Pet(x) ∧ ¬Mammal(x)) | null | null | null | null | null | null | null | null | null | null | null | null |
concl_256_46 | No pets are cats. | ∀x (Pet(x) → ¬Cat(x)) | no | null | null | null | ∀x (Pet(x) → ¬Cat(x)) | null | Uncertain | Uncertain | Uncertain | null | null | null | null | null | null | null | null |
story_159 | There are four seasons in a year: Spring, Summer, Fall, and Winter. All students who want to have a long vacation have summer as their favorite season. Emma's favorite season is summer. Mia's favorite season is not the same as Emma's. James wants to have a long vacation. | Season(spring) ∧ Season(summer) ∧ Season(fall) ∧ Season(winter) ∧ ∀x (Season(x) → (x = spring ∨ x = summer ∨ x = fall ∨ x = winter)) ∧ ∀x (Student(x) ∧ Want(x, longVacation) → Favorite(x, summer)) ∧ Favorite(emma, summer) ∧ ∀x ∀y (Season(x) ∧ Season(y) ∧ Favorite(mia, x) ∧ Favorite(emma, y) → ¬(x=y)) ∧ Want(james, long... | yes | null | null | 1. Spring, Summer, Fall, and Winter are all seasons (∧ adopted) and the only ones 2. Translation Failure (Premise 2): Added the missing 'Student(x)' predicate to match the NL text 'All students who...'. 4. Broken Linkage (Premise 2 & 5): Corrected casing mismatch from 'longvacation' to 'longVacation'. | Season(spring) ∨ Season(summer) ∨ Season(fall) ∨ Season(winter) ∧ (Season(spring) → ¬Season(summer) ∧ ¬Season(fall) ∧ ¬Season(winter)) ∧ (Season(summer) → ¬Season(spring) ∧ ¬Season(fall) ∧ ¬Season(winter)) ∧ (Season(fall) → ¬Season(spring) ∧ ¬Season(summer) ∧ ¬Season(winter)) ∧ (Season(winter) → ¬Season(spring) ∧ ¬Seas... | null | null | null | null | null | null | null | null | null | null | null | null |
concl_159_47 | James's favorite season is summer. | Favorite(james, summer) | no | null | null | Label corrected from True to Uncertain. Premise 2 restricts the rule to 'All students', but there is no premise explicitly stating that James is a student. Deducing this conclusion without the Student(james) constraint is a logical fallacy. | Favorite(james, summer) | Uncertain | True | Uncertain | Uncertain | null | null | null | null | null | null | null | null |
concl_159_48 | Mia's favorite season is spring. | Favorite(mia, spring) | no | null | null | null | Favorite(mia, spring) | Uncertain | Uncertain | Uncertain | Uncertain | null | null | null | null | null | null | null | null |
story_343 | No digital media are analog. Every printed text is analog media. All streaming services are digital media. If an object is a hardcover book, then it is printed text. If 1984 is a streaming service, then 1984 is a hardcover book. | ∀x (DigitalMedia(x) → ¬AnalogMedia(x)) ∧ ∀x (PrintedText(x) → AnalogMedia(x)) ∧ ∀x (StreamingService(x) → DigitalMedia(x)) ∧ ∀x (HardcoverBook(x) → PrintedText(x)) ∧ (StreamingService(y1984) → HardcoverBook(y1984)) | yes | null | null | ontology : Only changed '1984' with 'y1984' to avoid conflict with z3-parser | ∀x (DigitalMedia(x) → ¬AnalogMedia(x))
∀x (PrintedText(x) → AnalogMedia(x))
∀x (StreamingService(x) → DigitalMedia(x))
∀x (HardcoverBook(x) → PrintedText(x))
StreamingService(1984) → HardcoverBook(1984) | null | null | null | null | null | null | null | null | null | null | null | null |
concl_343_49 | 1984 is printed text. | PrintedText(y1984) | yes | null | null | ontology | PrintedText(1984) | Uncertain | Uncertain | Uncertain | Uncertain | null | null | null | null | null | null | null | null |
concl_343_50 | 1984 is a streaming service. | StreamingService(y1984) | yes | null | null | ontology | StreamingService(1984) | False | False | False | False | null | null | null | null | null | null | null | null |
concl_343_51 | 1984 is not a streaming service. | ¬StreamingService(y1984) | yes | null | null | ontology | ¬StreamingService(1984) | True | True | True | True | null | null | null | null | null | null | null | null |
story_213 | All Romance languages are Indo-European languages. Romance languages are a language family. All languages within a language family are related to each other. French and Spanish are both Romance languages. German is related to Spanish. Basque is not related to any other language. | ∀x (RomanceLanguage(x) → IndoEuropeanLanguage(x)) ∧ ∀x (RomanceLanguage(x) → MemberOf(x, romanceFamily)) ∧ ∀x ∀y ∀z ((MemberOf(x, z) ∧ MemberOf(y, z)) → (Related(x, y) ∧ Related(y, x))) ∧ RomanceLanguage(french) ∧ RomanceLanguage(spanish) ∧ Related(german, spanish) ∧ ∀x (x ≠ basque → ¬Related(basque, x)) | yes | null | null | 1. Broken Linkage (Premise 2): Replaced the generic constant 'languageFamily' with the specific 'romanceFamily'. Using a generic constant would incorrectly assign all language families in the domain to a single object. 2. Translation Failure & Broken Linkage (Premise 6): The original translation introduced an undefine... | ∀x (RomanceLanguage(x) → IndoEuropeanLanguage(x))
∀x (RomanceLanguage(x) → MemberOf(x, languageFamily))
∀x ∀y ∀z ((MemberOf(x, z) ∧ MemberOf(y, z)) → (Related(x, y) ∧ Related(y, x)))
RomanceLanguage(french) ∧ RomanceLanguage(spanish)
Related(german, spanish)
∀x (Language(x) → ¬Related(basque, x)) | null | null | null | null | null | null | null | null | null | null | null | null |
concl_213_52 | Basque is a Romance language. | RomanceLanguage(basque) | no | null | null | null | RomanceLanguage(basque) | False | False | Uncertain | False | The label 'False' is correct: if Basque were a Romance language, it would be a member of romanceFamily (premise 2), and hence related to French and Spanish (premise 3). But premise 6 states Basque is not related to any language, yielding a contradiction. Therefore RomanceLanguage(basque) is refutable. | null | null | (french ≠ basque) | null | null | null | null |
concl_213_53 | German is a Romance language. | RomanceLanguage(german) | no | null | null | null | RomanceLanguage(german) | Uncertain | Uncertain | Uncertain | Uncertain | The label 'Uncertain' is correct: the premises establish that German is related to Spanish, but relatedness is not sufficient to establish Romance language membership — the Related predicate is introduced for German only via premise 5 as a bare fact, not derived from family membership. Nothing in the premises rules out... | null | null | null | null | null | null | null |
concl_213_54 | French is an Indo-European language. | IndoEuropeanLanguage(french) | no | null | null | null | IndoEuropeanLanguage(french) | True | True | True | True | The label 'True' is directly derivable: premise 4 establishes RomanceLanguage(french), and premise 1 states ∀x (RomanceLanguage(x) → IndoEuropeanLanguage(x)), so IndoEuropeanLanguage(french) follows by universal instantiation and modus ponens. | null | null | null | null | null | null | null |
story_79 | Robert Lewandowski is a striker. Strikers are soccer players. Robert Lewandowski left Bayern Munchen. If a player leaves a team they no longer play for that team. | Striker(robertLewandowski) ∧ ∀x (Striker(x) → SoccerPlayer(x)) ∧ Left(robertLewandowski, bayernMunchen) ∧ ∀x ∀y (Player(x) ∧ Team(y) ∧ Left(x, y) → ¬PlaysFor(x, y)) | yes | null | null | Translation Failure (Premise 4): The original FOL '∀x ∀y (Left(x, y) → ¬PlaysFor(x, y))' ignored the explicit domain constraints 'player' and 'team' from the NL text ('If a player leaves a team...'). Corrected to '∀x ∀y (Player(x) ∧ Team(y) ∧ Left(x, y) → ¬PlaysFor(x, y))' to maintain absolute semantic fidelity to the ... | Striker(robertLewandowski)
∀x (Striker(x) → SoccerPlayer(x))
Left(robertLewandowski, bayernMunchen)
∀x ∀y (Left(x, y) → ¬PlaysFor(x, y)) | null | null | null | null | null | null | null | null | null | null | null | null |
concl_79_55 | Robert Lewandowski is a soccer player. | SoccerPlayer(robertLewandowski) | no | null | null | null | SoccerPlayer(robertLewandowski) | True | True | True | True | null | null | null | null | null | null | null | null |
concl_79_56 | Robert Lewandowski plays for Bayern Munchen. | PlaysFor(robertLewandowski, bayernMunchen) | no | null | null | Label corrected from False to Uncertain. With Premise 4 strictly translated to require Player(x) and Team(y), we cannot logically deduce that Lewandowski does not play for Bayern Munchen. There is no premise stating that Bayern Munchen is a 'Team' (Team(bayernMunchen)), nor one stating Lewandowski is a 'Player' (we onl... | PlaysFor(robertLewandowski, bayernMunchen) | Uncertain | False | False | Uncertain | null | null | null | null | null | null | null | null |
concl_79_57 | Robert Lewandowski is a star. | Star(robertLewandowski) | yes | null | null | Translation Failure: The NL simply says 'is a star', but the original FOL hallucinated the more specific predicate 'SoccerStar'. Corrected the FOL to the strictly literal 'Star(robertLewandowski)'. The label remains Uncertain. | SoccerStar(robertLewandowski) | Uncertain | Uncertain | Uncertain | Uncertain | null | null | null | null | null | null | null | null |
story_2 | Billings is a city in the state of Montana in U.S. The state of Montana includes the cities of Butte, Helena, and Missoula. White Sulphur Springs and Butte are cities in the same state in U.S. The city of St Pierre is not in the state of Montana. Any city in Butte is not in St Pierre. A city can only be in one state in... | City(billings) ∧ In(billings, montana) ∧ State(montana) ∧ City(butte) ∧ In(butte, montana) ∧ City(helena) ∧ In(helena, montana) ∧ City(missoula) ∧ In(missoula, montana) ∧ ∃x (City(whiteSulphurSprings) ∧ In(whiteSulphurSprings, x) ∧ City(butte) ∧ In(butte, x) ∧ State(x)) ∧ City(stPierre) ∧ ¬(In(stPierre, montana)) ∧ ∀x ... | yes | null | null | 1. Broken Linkage (Premises 4 & 5): Replaced the mismatched constant 'pierre' with 'stPierre' to correctly link with the conclusions. 2. Scope & Syntax Error (Premise 6): The original FOL '∀x ∃y ((City...' contained an unbalanced parenthesis and mis-scoped 'y' as an existential variable, leaving it unbound in the conse... | City(billings) ∧ In(billings, montana)
City(butte) ∧ In(butte, montana) ∧ City(helena) ∧ In(helena, montana) ∧ City(missoula) ∧ In(missoula, montana)
∃x (City(whitesulphursprings) ∧ In(whitesulphursprings, x) ∧ City(butte) ∧ In(butte, x))
City(pierre) ∧ ¬(In(pierre, montana))
∀x ((City(x) ∧ City(butte) ∧ In(x, butte)) ... | null | null | null | null | null | null | null | null | null | null | null | null |
concl_2_58 | Butte and St Pierre are in the same state. | ∃x (State(x) ∧ In(butte, x) ∧ In(stPierre, x)) | yes | null | null | null | ∃x (In(butte, x) ∧ In(stPierre, x)) | False | False | not_parsable | False | null | null | null | ¬(butte=bristol) ∧ ¬(butte=texarkana) ∧ ¬(butte=texhoma) ∧ ¬(butte=unionCity) ∧ ¬(stPierre=bristol) ∧ ¬(stPierre=texarkana) ∧ ¬(stPierre=texhoma) ∧ ¬(stPierre=unionCity) | null | null | null | null |
concl_2_59 | St Pierre and Bismarck are in the same state. | ∃x (In(stPierre, x) ∧ In(bismarck, x) ∧ State(x)) | yes | null | null | Broken Linkage: The original FOL used 'pierre', but the conclusions (and updated premises) standardise on 'stPierre'. Corrected to 'stPierre' to fix the broken logical chain. Modified also the ontology State. (2) Removed also the fact that these two are cities (not explicitely said in NL) | ∃x (City(pierre) ∧ In(pierre, x) ∧ City(bismarck) ∧ In(bismarck, x)) | Uncertain | Uncertain | not_parsable | Uncertain | null | null | null | null | null | null | null | null |
concl_2_60 | Montana is home to the city of Missoula. | City(missoula) ∧ In(missoula, montana) | no | null | null | null | City(missoula) ∧ In(missoula, montana) | True | True | not_parsable | True | null | null | null | null | null | null | null | null |
story_192 | International students in the US have either an F1 visa or a J1 visa. An international student in the US with an F1 visa needs to apply for CPT or OPT if the student wants to work in the US. Mike is an international student. Mike needs to apply for CPT if he wants to work in the US. | ∀x (InternationalStudent(x) ∧ In(x, unitedStates) → F1Visa(x) ⊕ J1Visa(x)) ∧ ∀x (InternationalStudent(x) ∧ In(x, unitedStates) ∧ F1Visa(x) ∧ WantToWorkIn(x, unitedStates) → Apply(x, cpt) ∨ Apply(x, opt)) ∧ InternationalStudent(mike) ∧ WantToWorkIn(mike, unitedStates) → Apply(mike, cpt) | yes | true | null | 1. Scope Error (Premise 4): The original FOL 'WantToWorkIn(x, unitedStates) → Apply(mike, cpt)' used a free, unbound variable 'x' in the antecedent while referring to the constant 'mike' in the consequent. Corrected to 'WantToWorkIn(mike, unitedStates)' to accurately match the NL text. | ∀x (InternationalStudent(x) ∧ In(x, unitedStates) → F1Visa(x) ⊕ J1Visa(x))
∀x (InternationalStudent(x) ∧ In(x, unitedStates) ∧ F1Visa(x) ∧ WantToWorkIn(x, unitedStates) → Apply(x, cpt) ∨ Apply(x, opt))
InternationalStudent(mike)
WantToWorkIn(x, unitedStates) → Apply(mike, cpt) | null | null | null | null | null | null | null | null | either_or | null | null | null |
concl_192_61 | Mike has an F1 visa. | F1Visa(mike) | no | null | null | null | F1Visa(mike) | Uncertain | Uncertain | Uncertain | Uncertain | null | null | null | null | null | null | null | null |
concl_192_62 | Mike has a J1 visa. | J1Visa(mike) | no | null | null | null | J1Visa(mike) | Uncertain | Uncertain | Uncertain | Uncertain | null | null | null | null | null | null | null | null |
story_442 | All Brown Swiss cattle are cows. Some pets are Brown Swiss cattle. All cows are domesticated animals. Alligators are not domesticated animals. Ted is an alligator. | ∀x (BrownSwissCattle(x) → Cow(x)) ∧ ∃x (Pet(x) ∧ BrownSwissCattle(x)) ∧ ∀x (Cow(x) → DomesticatedAnimal(x)) ∧ ∀x (Alligator(x) → ¬DomesticatedAnimal(x)) ∧ Alligator(ted) | yes | true | some_plural | Typo Correction: The original FOL misspelled 'Alligator' as 'Aligator' in Premises 4 and 5. Corrected to 'Alligator' to maintain strict semantic alignment with the standard spelling in the Natural Language text. | ∀x (BrownSwissCattle(x) → Cow(x))
∃x (Pet(x) ∧ BrownSwissCattle(x))
∀x (Cow(x) → DomesticatedAnimal(x))
∀x (Aligator(x) → ¬DomesticatedAnimal(x))
Aligator(ted) | null | null | null | null | null | null | null | null | null | null | null | null |
concl_442_63 | Ted is a pet. | Pet(ted) | no | null | null | null | Pet(ted) | Uncertain | Uncertain | Uncertain | Uncertain | null | null | null | null | null | null | null | null |
concl_442_64 | Ted is a pet and Brown Swiss cattle. | Pet(ted) ∧ BrownSwissCattle(ted) | no | null | null | null | Pet(ted) ∧ BrownSwissCattle(ted) | False | False | False | False | null | null | null | null | null | null | null | null |
concl_442_65 | If Ted is a Brown Swiss cattle, then Ted is not a pet. | BrownSwissCattle(ted) → ¬Pet(ted) | no | null | null | null | BrownSwissCattle(ted) → ¬Pet(ted) | True | True | True | True | null | null | null | null | null | null | null | null |
story_234 | Yale University is a private Ivy League research university. Yale University moved to New Haven in 1716. Yale University's endowment was valued at $42.3 billion. A list of residential colleges at Yale: Benjamin Franklin College, Berkeley College, Branford College, Davenport College, Ezra Stiles College, Grace Hopper Co... | PrivateIvyLeagueResearchUniversity(yaleUniversity) ∧ MovedTo(yaleUniversity, newHaven) ∧ MovedIn(yaleUniversity, year1716) ∧ ValuedAt(yaleUniversitysEndowment, usd42point3billion) ∧ ResidentialCollege(benjaminFranklinCollege) ∧ At(benjaminFranklinCollege, yaleUniversity) ∧ ResidentialCollege(berkeleyCollege) ∧ At(berke... | yes | null | null | 1. Translation Failure / Category Error (Premise 4): The original FOL used a universal conditional that failed to assert the existence of the colleges, making Conclusion 68 unprovable. It also treated specific college entities as unary properties instead of constants. Replaced with a single conjunction of ground facts ... | PrivateIvyLeagueResearchUniversity(yaleUniversity)
MovedTo(yaleUniversity, newHaven) ∧ MovedIn(yaleUniversity, year1716)
ValuedAt(yaleUniversitysEndowment, 42point3billion)
∀x (ResidentialCollege(x) → At(x, yale) ∧ (BenjaminFranklinCollege(x) ⊕ BerkleyCollege(x) ⊕ BranfordCollege(x) ⊕ DavenportCollege(x) ⊕ EzraStilesCo... | null | null | null | null | null | null | null | null | null | null | null | null |
concl_234_66 | A private Ivy League research university moved to New Haven. | ∃x (PrivateIvyLeagueResearchUniversity(x) ∧ MovedTo(x, newHaven)) | no | null | null | null | ∃x (PrivateIvyLeagueResearchUniversity(x) ∧ MovedTo(x, newHaven)) | True | True | True | True | null | null | null | null | null | null | null | null |
concl_234_67 | Yale University has the largest university endowment of any educational institution. | LargestUniversityEndowmentOf(yaleUniversity, anyEducationalInstitution) | yes | null | null | Broken Linkage: The original FOL uses 'yale' instead of 'yaleUniversity' as the constant. Unified to 'yaleUniversity' to match the premises. | LargestUniversityEndowmentOf(yale, anyEducationalInstitution) | Uncertain | Uncertain | Uncertain | Uncertain | null | null | null | null | null | null | null | null |
concl_234_68 | Pierson College is a residential college at Yale. | ResidentialCollege(piersonCollege) ∧ At(piersonCollege, yaleUniversity) | yes | null | null | Identified 'yale' and 'yaleUniversity' | ResidentialCollege(piersonCollege) ∧ At(piersonCollege, yale) | True | True | Uncertain | True | null | null | null | null | null | null | null | null |
story_120 | Badults is a British Sitcom series starring members of Pappy's. Badults was piloted in July 2013 on BBC Three. The working title 'The Secret Dude Society' was used for Badults. Andrew Collins was the script editor for Badults. | ∃x (BritishSitcom(badults) ∧ Series(badults) ∧ MemberOf(x, pappys) ∧ Star(x, badults)) ∧ PilotedIn(badults, july2013) ∧ PilotedOn(badults, bBCThree) ∧ WorkingTitle(theSecretDudeSociety, badults) ∧ UsedFor(theSecretDudeSociety, badults) ∧ ScriptEditorFor(andrewCollins, badults) | yes | null | null | null | ∃x (BritishSitcom(badults) ∧ Series(badults) ∧ MemberOf(x, pappys) ∧ Starring(badults, x))
PilotedIn(badults, july2013) ∧ PilotedOn(badults, bBCThree)
WorkingTitle(theSecretDudeSociety, badults) ∧ UsedFor(theSecretDudeSociety, badults)
ScriptEditorFor(andrewCollins, badults) | null | null | null | null | null | null | null | null | null | ontology_correction | null | null |
concl_120_69 | Andrew Collins was the script editor for a series with the working title 'The Secret Dude Society'. | ∃x (ScriptEditorFor(andrewCollins, x) ∧ Series(x) ∧ WorkingTitle(theSecretDudeSociety, x)) | no | null | null | null | ∃x (ScriptEditorFor(andrewCollins, x) ∧ Series(x) ∧ WorkingTitle(theSecretDudeSociety, x)) | True | True | True | True | null | null | null | null | null | null | null | null |
concl_120_70 | No members of Pappy's have starred in a show piloting on BBC Two or BBC Three. | ∀x ∀y (MemberOf(x, pappys) ∧ Star(x, y) → ¬(PilotedOn(y, bBCTwo) ∨ PilotedOn(y, bBCThree))) | no | null | null | null | ∀x ∀y (MemberOf(x, pappys) ∧ Starring(y, x) → ¬(PilotedOn(y, bBCTwo) ∨ PilotedOn(y, bBCThree))) | False | False | False | False | null | null | null | null | null | null | null | null |
story_322 | All growth stocks are bought to earn profits from rapid price appreciation. If a stock is bought to earn profits from rapid price appreciation, then it is not suitable for a retirement fund. Some stocks are growth stocks. All mature stocks are suitable for a retirement fund. KO is a mature stock. | ∀x ((Stock(x) ∧ Growth(x)) → BoughtToEarnProfitFrom(x, rapidPriceAppreciation)) ∧ ∀x ((Stock(x) ∧ BoughtToEarnProfitFrom(x, rapidPriceAppreciation)) → ¬SuitableFor(x, retirementFund)) ∧ ∃x (Stock(x) ∧ Growth(x)) ∧ ∀x ((Stock(x) ∧ Mature(x)) → SuitableFor(x, retirementFund)) ∧ Stock(kO) ∧ Mature(kO) | yes | true | some_plural | 1. Compositional Semantics / Translation Failure: Based on the insight that 'growth stock' and 'mature stock' intrinsically imply being a 'stock', the monolithic predicates 'GrowthStock(x)' and 'MatureStock(x)' have been decomposed into 'Stock(x) ∧ Growth(x)' and 'Stock(x) ∧ Mature(x)'. This ensures the domain constrai... | ∀x (GrowthStock(x) → BoughtToEarnProfitFrom(x, rapidPriceAppreciation))
∀x (BoughtToEarnProfitFrom(x, earnProfit, rapidPriceAppreciation) → ¬SuitableFor(x, retirementFund))
∃x (Stock(x) ∧ GrowthStock(x))
∀x (MatureStock(x) → SuitableFor(x, retirementFund))
MatureStock(kO) | null | null | null | null | null | null | null | null | null | null | null | null |
concl_322_71 | KO is a stock. | Stock(kO) | no | null | null | With the compositional decomposition of 'MatureStock(kO)' into 'Stock(kO) ∧ Mature(kO)' in Premise 5, it is now explicitly established that KO is a stock. The label is therefore corrected from Uncertain to True. | Stock(kO) | True | Uncertain | True | True | null | null | null | null | null | null | null | null |
concl_322_72 | KO is a stock and a growth stock. | Stock(kO) ∧ Growth(kO) | yes | null | null | 1. Translation Failure: The original FOL '¬GrowthStock(kO)' directly contradicted the positive phrasing of the NL. Corrected to 'Stock(kO) ∧ Growth(kO)' to strictly map the text. 2. Logic Check: The label 'False' is logically sound because assuming KO is a Growth stock triggers a contradiction: Premise 1 forces BoughtT... | ¬GrowthStock(kO) | False | False | True | False | null | null | null | null | null | null | null | null |
concl_322_73 | If KO is a growth stock or bought to earn profits from rapid price appreciation, then KO is neither a stock nor is its price volatile. | ((Stock(kO) ∧ Growth(kO)) ∨ BoughtToEarnProfitFrom(kO, rapidPriceAppreciation)) → (¬Stock(kO) ∧ ¬VolatilePrice(kO)) | yes | null | null | 1. Translation Failure: Applied the 'Stock ∧ Growth' decomposition. 2. Broken Linkage: Fixed the ternary 'BoughtToEarnProfitFrom' predicate to binary. 3. Translation Failure: Replaced '¬BoughtToEarnProfitFrom' in the consequent with '¬VolatilePrice(kO)' to accurately capture 'nor is its price volatile'. 4. Scope: Added... | GrowthStock(kO) ∨ BoughtToEarnProfitFrom(kO, earnProfit, rapidPriceAppreciation) → ¬Stock(kO) ∧ ¬BoughtToEarnProfitFrom(kO, rapidPriceAppreciation) | True | True | True | True | null | null | null | null | null | null | null | null |
story_83 | All vehicle registration plates in Istanbul begin with the number 34. Plates that do not begin with the number 34 are not from Istanbul. Joe's vehicle registration plate is from Istanbul. Tom's license plate begins with the number 35. If a license plate begins with the number 35, then it does not begin with the number ... | ∀x (VehicleRegistrationPlateIn(x, istanbul) → BeginWith(x, num34)) ∧ ∀x (¬BeginWith(x, num34) → ¬VehicleRegistrationPlateIn(x, istanbul)) ∧ ∃x (Owns(joe, x) ∧ VehicleRegistrationPlateIn(x, istanbul)) ∧ ∃x ∃y (Owns(tom, x) ∧ VehicleRegistrationPlateIn(x, y) ∧ BeginWith(x, num35)) ∧ ∀x (BeginWith(x, num35) → ¬BeginWith(x... | yes | null | null | Broken Linkage (Premise 2): The original FOL used 'FromIstanbul(x)', which disconnected it from the 'VehicleRegistrationPlateIn(x, istanbul)' predicate used in Premise 1, Premise 3, and Conclusion 75. Unified the predicate to 'VehicleRegistrationPlateIn(x, istanbul)' to allow the logical chain to resolve. Note: The pre... | ∀x (VehicleRegistrationPlateIn(x, istanbul) → BeginWith(x, num34))
∀x (¬BeginWith(x, num34) → ¬FromIstanbul(x))
∃x (Owns(joe, x) ∧ VehicleRegistrationPlateIn(x, istanbul))
∃x (Owns(tom, x) ∧ BeginWith(x, num35))
∀x (BeginWith(x, num35) → ¬BeginWith(x, num34)) | null | null | null | null | null | null | null | null | null | null | null | null |
End of preview.
Data from the paper "Fixing FOLIO and MALLS: Verified Annotations and an LLM-assisted Framework to Focus Human Relabeling" (https://arxiv.org/pdf/2606.02837)
FOLIO — Curated Pairs and Signatures
Curated FOLIO instances (validation split) for evaluating LLM-based first-order-logic (FOL) formula curation.
Each instance pairs a natural-language sentence with the original FOL formalization (FOL_sentence_old) and a curated reference (FOL_sentence), grouped by story;
NLI labels (True, False or Unknown) are corrected and provided in this curated version for each conclusion.
per-story ontologies (signatures) are provided separately.
Configurations
FOLIO_instances — FOLIO_instances.jsonl
275 instances used for held-out evaluation.
| Field | Type | Description |
|---|---|---|
id |
string | Instance id (e.g. story_380, concl_380_1) |
NL_sentence |
string | Natural-language sentence |
FOL_sentence |
string | Curated reference FOL formalization |
FOL_sentence_old |
string | Original (pre-curation) FOL formalization |
corrected |
bool | Whether the original was corrected |
ambiguity |
bool | Whether the sentence is ambiguous |
ambiguity_explanation |
string | Rationale for the ambiguity flag (when applicable) |
correction_explanation |
string | Rationale for the correction (selection only) |
label |
string | Gold NLI label for the curated formula (FOL_sentence). |
label_z3 |
string | Z3-derived NLI label for the curated formula. |
label_old |
string | Original NLI label from the original formula (FOL_sentence_old). |
label_old_z3 |
string | Z3-derived NLI label for the original formula. |
labelled signature — FOLIO_ontology.jsonl
Per-story ontology used to render vocabulary blocks in prompts and to type-check formulas. One JSON object per line, 73 stories.
| Field | Type | Description |
|---|---|---|
story_id |
int | Story id (matches the *_{story_id} suffix in rawpairs_*.id) |
Rel |
object | {predicate_name → {arity, pos_meaning, neg_meaning}} |
Const |
object | {constant_name → description} |
FOL syntax
Unicode operators:
- Quantifiers:
∀,∃ - Boolean:
¬,∧,∨,→,↔,⊕ - Predicates: capitalized (e.g.
Human(x)) - Variables: lowercase; constants: capitalized
Citation
If you want to cite the full work or use the dataset, please refer to https://arxiv.org/pdf/2606.02837
@misc{brunello2026fixingfoliomallsverified,
title={Fixing FOLIO and MALLS: Verified Annotations and an LLM-assisted Framework to Focus Human Relabeling},
author={Andrea Brunello and Cristian Curaba and Luca Geatti and Michele Mignani and Angelo Montanari and Nicola Saccomanno},
year={2026},
eprint={2606.02837},
archivePrefix={arXiv},
primaryClass={cs.CL},
url={https://arxiv.org/abs/2606.02837},
}
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