DSAVlab-UNIUD/FOLIO_validation-curated huggingface dataset:
Sentence: Beethoven is not a conductor.
FOL: ¬Conductor(beethoven)
Correction notes: 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 prove he is not. Changed label to Uncertain.
Sentence: 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 of Kelly Wearstler's design styles that Max adores are dreamy. If a design by Max that he adores has interesting geometries, then the design is a brutalist building and evocative.
FOL: ∀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(max, x) ∧ KellyWearstler(x) ∧ DesignStyle(x) → Dreamy(x)) ∧ ∀x (Adore(max, x) ∧ Design(x) ∧ ByMax(x) ∧ InterestingGeometry(x) → BrutalistBuilding(x) ∧ Evocative(x))
Correction notes: 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 conditional generalisation — and in fact '∃x (P ∧ Q → R)' is logically equivalent to '∃x (¬(P ∧ Q) ∨ R)', which is almost trivially true and does not capture the intended universal conditional. The NL reads as a general rule ('if a design... then...'), so the correct quantifier is ∀, giving '∀x (Adore(max, x) ∧ Design(x) ∧ ByMax(x) ∧ InterestingGeometry(x) → BrutalistBuilding(x) ∧ Evocative(x))'.
Sentence: A design by Max is a brutalist building.
FOL: ∃x (Design(x) ∧ ByMax(x) ∧ BrutalistBuilding(x))
Label: Uncertain
Sentence: A design by Max is evocative and dreamy.
FOL: ∃x (Design(x) ∧ ByMax(x) ∧ Evocative(x) ∧ Dreamy(x))
Correction notes: 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 ByMax to the Dreamy property (which requires KellyWearstler). Because we cannot prove the existence of such an entity, the label must be Uncertain. IF THE INTERPRETATION IS UNIVERSAL: then however, any premise talks about designs by Max that he adores, so it can be True, since nothing informed us about the objects x that satisfy only the properties Design(x) ∧ ByMax(x)
Sentence: A design by Max is either evocative or dreamy.
FOL: ∃x (Design(x) ∧ ByMax(x) ∧ (Evocative(x) ⊕ Dreamy(x)))
Correction notes: 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 don't even know if he has designs at all, the solver cannot definitively prove this False. The label must be Uncertain. Same as before, even considering the other interpretation
Sentence: 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 at Roland Garros 2022 are either female or male. All male tennis players at Roland Garros in 2022 lost to Rafael Nadal. If Coco Gauff is ranked highly by the Women's Tennis Association or lost to Rafael Nadal, then Coco Gauff is not a male tennis player at Roland Garros 2022. Coco Gauff is at Roland Garros 2022.
FOL: ∀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)) → (FemaleTennisPlayer(x) ⊕ MaleTennisPlayer(x))) ∧ ∀x ((MaleTennisPlayer(x) ∧ At(x, rolandGarros2022)) → LostTo(x, nadal, rolandGarros2022)) ∧ ((RankedHighlyBy(cocoGauff, womensTennisAssociation) ∨ LostTo(cocoGauff, nadal, rolandGarros2022)) → ¬(MaleTennisPlayer(cocoGauff) ∧ At(cocoGauff, rolandGarros2022))) ∧ TennisPlayer(cocoGauff) ∧ At(cocoGauff, rolandGarros2022)
Correction notes: 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 Nadal' as 'świątek'. Corrected to 'nadal'. (3) Syntax/Translation: Premise 6 was completely broken, using wrong constants ('świątek' instead of 'nadal') and wrong unary predicates ('AtRolandGarros2022(x)'). Standardized to match the established premises, and added strict grouping parentheses to the antecedent to ensure standard parser precedence. (4) the property 'x losts to y at z' were translated as LostTo(x, y) ∧ At(x, z), that is not the correct formalization. Now it is fixed extending LostTo as a ternary binary.
Sentence: Coco Gauff is among the most active major tennis players.
FOL: MostActivePlayerIn(cocoGauff, majorTennis)
Correction notes: 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.
Sentence: Coco Gauff has lost to Rafael Nadal.
FOL: ∃x LostTo(cocoGauff, nadal, x)
Correction notes: 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.
Sentence: 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.
FOL: ¬LostTo(cocoGauff, świątek, rolandGarros2022) ∨ ¬MostActivePlayerIn(cocoGauff, majorTennis)
Correction notes: ontology_correction
Sentence: All cats are mammals. Some pets are not mammals.
FOL: ∀x (Cat(x) → Mammal(x)) ∧ ∃x (Pet(x) ∧ ¬Mammal(x))
Sentence: No pets are cats.
FOL: ∀x (Pet(x) → ¬Cat(x))
Sentence: 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.
FOL: 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, longVacation)
Correction notes:  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'.
Sentence: James's favorite season is summer.
FOL: Favorite(james, summer)
Label: Uncertain
Correction notes: 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.
Sentence: Mia's favorite season is spring.
FOL: Favorite(mia, spring)
Label: Uncertain
Sentence: 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.
FOL: ∀x (DigitalMedia(x) → ¬AnalogMedia(x)) ∧ ∀x (PrintedText(x) → AnalogMedia(x)) ∧ ∀x (StreamingService(x) → DigitalMedia(x)) ∧ ∀x (HardcoverBook(x) → PrintedText(x)) ∧ (StreamingService(y1984) → HardcoverBook(y1984))
Correction notes: ontology : Only changed '1984' with 'y1984' to avoid conflict with z3-parser
Sentence: 1984 is printed text.
FOL: PrintedText(y1984)
Label: Uncertain
Correction notes: ontology
Sentence: 1984 is a streaming service.
FOL: StreamingService(y1984)
Label: False
Correction notes: ontology
Sentence: 1984 is not a streaming service.
FOL: ¬StreamingService(y1984)
Label: True
Correction notes: ontology
Sentence: 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.
FOL: ∀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))
Correction notes: 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 undefined 'Language(x)' predicate. Since 'Language' is never linked to 'RomanceLanguage', it breaks the logical chain (we cannot prove French or Spanish are 'Languages' to trigger the rule). Furthermore, it ignored the word 'other'. Corrected to '∀x (x ≠ basque → ¬Related(basque, x))' to accurately capture 'any other' without hallucinating disconnected predicates.
Sentence: Basque is a Romance language.
FOL: RomanceLanguage(basque)
Label: False
Sentence: German is a Romance language.
FOL: RomanceLanguage(german)
Label: Uncertain
Sentence: French is an Indo-European language.
FOL: IndoEuropeanLanguage(french)
Label: True
Sentence: 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.
FOL: Striker(robertLewandowski) ∧ ∀x (Striker(x) → SoccerPlayer(x)) ∧ Left(robertLewandowski, bayernMunchen) ∧ ∀x ∀y (Player(x) ∧ Team(y) ∧ Left(x, y) → ¬PlaysFor(x, y))
Correction notes: 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 natural language, even if it changes downstream entailment.
Sentence: Robert Lewandowski is a soccer player.
FOL: SoccerPlayer(robertLewandowski)
Label: True
Sentence: Robert Lewandowski plays for Bayern Munchen.
FOL: PlaysFor(robertLewandowski, bayernMunchen)
Label: Uncertain
Correction notes: 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 only know 'SoccerPlayer'). Without these exact predicates established, the implication fails to trigger.
Sentence: Robert Lewandowski is a star.
FOL: Star(robertLewandowski)
Label: Uncertain
Correction notes: 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.
Sentence: 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 U.S. except for Bristol, Texarkana, Texhoma and Union City.
FOL: 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 ((City(x) ∧ City(butte) ∧ In(x, butte)) → ¬(In(x, stPierre))) ∧ ∀x ∀y ((City(x) ∧ State(y) ∧ In(x, y) ∧ ¬(x=bristol) ∧ ¬(x=texarkana) ∧ ¬(x=texhoma) ∧ ¬(x=unionCity)) → ¬∃z (¬(z=y) ∧ State(z) ∧ In(x, z)))
Correction notes: 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 consequent. Corrected the quantifier to '∀y' and removed the rogue parenthesis. 3. Invalid Swaps Reverted: Restored 'City(butte)' in Premise 5, which the previous reviewer invalidly removed as a logically equivalent swap.
Sentence: Butte and St Pierre are in the same state.
FOL: ∃x (State(x) ∧ In(butte, x) ∧ In(stPierre, x))
Label: False
Sentence: St Pierre and Bismarck are in the same state.
FOL: ∃x (In(stPierre, x) ∧ In(bismarck, x) ∧ State(x))
Label: Uncertain
Correction notes: 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)
Sentence: Montana is home to the city of Missoula.
FOL: City(missoula) ∧ In(missoula, montana)
Label: True
Sentence: 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.
FOL: ∀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)
Correction notes: 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.
Sentence: Mike has an F1 visa.
FOL: F1Visa(mike)
Label: Uncertain
Sentence: Mike has a J1 visa.
FOL: J1Visa(mike)
Label: Uncertain
Sentence: 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.
FOL: ∀x (BrownSwissCattle(x) → Cow(x)) ∧ ∃x (Pet(x) ∧ BrownSwissCattle(x)) ∧ ∀x (Cow(x) → DomesticatedAnimal(x)) ∧ ∀x (Alligator(x) → ¬DomesticatedAnimal(x)) ∧ Alligator(ted)
Correction notes: 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.
Sentence: Ted is a pet.
FOL: Pet(ted)
Label: Uncertain
Sentence: Ted is a pet and Brown Swiss cattle.
FOL: Pet(ted) ∧ BrownSwissCattle(ted)
Label: False
Sentence: If Ted is a Brown Swiss cattle, then Ted is not a pet.
FOL: BrownSwissCattle(ted) → ¬Pet(ted)
Label: True
Sentence: 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 College, Jonathan Edwards College, Morse College, Pauli Murray College, Pierson College, Saybrook College, Silliman College, Timothy Dwight College, and Trumbull College.
FOL: PrivateIvyLeagueResearchUniversity(yaleUniversity) ∧ MovedTo(yaleUniversity, newHaven) ∧ MovedIn(yaleUniversity, year1716) ∧ ValuedAt(yaleUniversitysEndowment, usd42point3billion) ∧ ResidentialCollege(benjaminFranklinCollege) ∧ At(benjaminFranklinCollege, yaleUniversity) ∧ ResidentialCollege(berkeleyCollege) ∧ At(berkeleyCollege, yaleUniversity) ∧ ResidentialCollege(branfordCollege) ∧ At(branfordCollege, yaleUniversity) ∧ ResidentialCollege(davenportCollege) ∧ At(davenportCollege, yaleUniversity) ∧ ResidentialCollege(ezraStilesCollege) ∧ At(ezraStilesCollege, yaleUniversity) ∧ ResidentialCollege(graceHopperCollege) ∧ At(graceHopperCollege, yaleUniversity) ∧ ResidentialCollege(jonathanEdwardsCollege) ∧ At(jonathanEdwardsCollege, yaleUniversity) ∧ ResidentialCollege(morseCollege) ∧ At(morseCollege, yaleUniversity) ∧ ResidentialCollege(pauliMurrayCollege) ∧ At(pauliMurrayCollege, yaleUniversity) ∧ ResidentialCollege(piersonCollege) ∧ At(piersonCollege, yaleUniversity) ∧ ResidentialCollege(saybrookCollege) ∧ At(saybrookCollege, yaleUniversity) ∧ ResidentialCollege(sillimanCollege) ∧ At(sillimanCollege, yaleUniversity) ∧ ResidentialCollege(timothyDwightCollege) ∧ At(timothyDwightCollege, yaleUniversity) ∧ ResidentialCollege(trumbullCollege) ∧ At(trumbullCollege, yaleUniversity)
Correction notes: 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 (e.g., 'ResidentialCollege(piersonCollege) ∧ At(piersonCollege, yale)') to properly ground the facts. 2. Typo (Premise 4): Corrected 'BerkleyCollege' to 'BerkeleyCollege' to match the NL. 4. Syntax Error (Premise 3): The constant '42point3billion' starts with a digit, which violates standard FOL syntax rules (for z3-parser). Renamed to 'usd42point3billion'. 5. Unified 'yale' and 'yaleUniversity'
Sentence: A private Ivy League research university moved to New Haven.
FOL: ∃x (PrivateIvyLeagueResearchUniversity(x) ∧ MovedTo(x, newHaven))
Label: True
Sentence: Yale University has the largest university endowment of any educational institution.
FOL: LargestUniversityEndowmentOf(yaleUniversity, anyEducationalInstitution)
Label: Uncertain
Correction notes: Broken Linkage: The original FOL uses 'yale' instead of 'yaleUniversity' as the constant. Unified to 'yaleUniversity' to match the premises.
Sentence: Pierson College is a residential college at Yale.
FOL: ResidentialCollege(piersonCollege) ∧ At(piersonCollege, yaleUniversity)
Label: True
Correction notes: Identified 'yale' and 'yaleUniversity'
Sentence: 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.
FOL: ∃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)
Sentence: Andrew Collins was the script editor for a series with the working title 'The Secret Dude Society'.
FOL: ∃x (ScriptEditorFor(andrewCollins, x) ∧ Series(x) ∧ WorkingTitle(theSecretDudeSociety, x))
Label: True
Sentence: No members of Pappy's have starred in a show piloting on BBC Two or BBC Three.
FOL: ∀x ∀y (MemberOf(x, pappys) ∧ Star(x, y) → ¬(PilotedOn(y, bBCTwo) ∨ PilotedOn(y, bBCThree)))
Label: False
Sentence: 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.
FOL: ∀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)
Correction notes: 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 constraint 'Stock' is universally active across all premises. 2. Translation Failure (Premise 2): Added the 'Stock(x)' constraint to match 'If a stock is bought...'. 3. Broken Linkage (Premise 2): Fixed the ternary 'BoughtToEarnProfitFrom' by removing the hallucinated 'earnProfit' argument to match Premise 1.
Sentence: KO is a stock.
FOL: Stock(kO)
Label: True
Correction notes: 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.
Sentence: KO is a stock and a growth stock.
FOL: Stock(kO) ∧ Growth(kO)
Label: False
Correction notes: 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 BoughtToEarnProfitFrom to be true, which (combined with Stock(kO)) forces ¬SuitableFor via Premise 2, directly contradicting the SuitableFor conclusion derived from Premises 4 and 5.
Sentence: 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.
FOL: ((Stock(kO) ∧ Growth(kO)) ∨ BoughtToEarnProfitFrom(kO, rapidPriceAppreciation)) → (¬Stock(kO) ∧ ¬VolatilePrice(kO))
Label: True
Correction notes: 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 required grouping parentheses around the antecedent. 5. Entailment Logic Evaluation: With the new compositional semantics, Stock(kO) is definitively True, making the consequent definitively False. Because KO is a Stock and is SuitableFor a retirement fund, BoughtToEarnProfitFrom MUST be definitively False (otherwise Premise 2 would trigger a contradiction). By extension, Growth(kO) must also be False. Thus, both sides of the antecedent's disjunction are definitively False, making the material implication vacuously True.