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Inception is not a folk song. | ¬FolkSong(inception) |
Inception is either a video or a folk song. | Video(inception) ⊕ FolkSong(inception) |
Mac is a video. | Video(mac) |
All inductive reasoning processes derive general principles from a body of observations. | ∀x (InductiveReasoning(x) → DeriveFrom(generalPrinciple, observations)) |
Two major types of reasoning rules are inductive reasoning and deductive reasoning. | ∀x (MajorArgumentForm(x) → (InductiveReasoning(x) ⊕ DeductiveReasoning(x)) |
All deductive reasoning processes are only based on facts and rules. | ∀x (DeductiveReasoning(x) → (BasedOn(x, fact) ∨ BasedOn(x, rule))) |
Nothing only based on facts and rules is used for statistical generalization. | ∀x ((BasedOn(x, fact) ∨ BasedOn(x, rule)) → (¬UsedFor(x, statisticalGeneralization))) |
Modus Ponens is not both used in inductive reasoning and used for statistical generalization. | ¬(InductiveReasoning(modusPonens) ∧ UsedFor(modusPonens, statisticalGeneralization)) |
Modus Ponens is a component of a major part of reasoning rule. | ArgumentForm(modusPonens) |
Reasoning with Modus Ponens is based on facts and rules. | BasedOn(x, fact) ∨ BasedOn(x, rule) |
Modus Ponens derives general principles from a body of observations and is used for statistical generalization. | DeriveFrom(generalPrinciple, observations) ∧ UsedFor(x, statisticalGeneralization) |
If Modus Ponens either derives general principles from a body of observations and is used for statistical generalization, or neither, then Modus Ponens is is neither used in inductive reasoning nor used for statistical generalization. | ¬(Derive(generalPrinciple, observations) ⊕ UsedFor(x, statisticalGeneralization)) → (¬InductiveReasoning(modusPonens) ∧ (¬UsedFor(modusPonens, statisticalGeneralization))) |
No trick-shot artist in Yale's varsity team struggles with half court shots. | ∀x ((In(x, yaleSVarsityTeam) ∧ TrickShotArtist(x)) → ¬StruggleAt(x, halfCourtShot)) |
Everyone on Yale's varsity team is someone who struggles with half court shots or who successfully shoots a high percentage of 3-pointers. | ∀x (In(x, yaleSVarsityTeam) → (StruggleAt(x, halfCourtShot) ∨ GoodAt(x, threes))) |
Everyone on Yale's varsity team who successfully shoots a high percentage of 3-pointers is solid at shooting 2-pointers. | ∀x ((In(x, yaleSVarsityTeam) ∧ GoodAt(x, threes)) → GoodAt(x, twos)) |
No one on Yale's varsity team who is solid at shooting 2-pointers is bad at mid-range shots. | ∀x ((In(x, yaleSVarsityTeam) ∧ GoodAt(x, twos)) → BadAt(x, midRangeShot)) |
Jack is on Yale's varsity team, and he is either a trick-shot artist or he successfully shoots a high percentage of 3-pointers. | In(jack, yaleSVarsityTeam) ∧ (TrickShotArtist(jack) ⊕ GoodAt(jack, threes)) |
Jack struggles at half court shots. | StruggleAt(jack, halfCourtShot) |
Jack is bad at mid-range shots. | BadAt(jack, midRangeShot) |
Jack is solid at shooting 2-pointers or bad at mid-range shots. | GoodAt(jack, twos) ∨ BadAt(jack, midRangeShot) |
Jack is either solid at shooting 2-pointers or bad at mid-range shots. | GoodAt(jack, twos) ⊕ BadAt(jack, midRangeShot) |
Jack is a trick-shot artist or bad at mid-range shots. | TrickShotArtist(jack) ∨ BadAt(jack, midRangeShot)) |
Jack is either a trick-shot artist or bad at mid-range shots. | TrickShotArtist(jack) ⊕ BadAt(jack, midRangeShots) |
Jack is either a player who successfully shoots a high percentage of 3-pointers or is bad at mid-range shots. | GoodAt(jack, threes) ⊕ BadAt(jack, midRangeShot) |
If Jack is not solid at shooting 2-pointers and bad at mid-range shots, then Jack is not solid at shooting 2-pointers and is a player who successfully shoots a high percentage of 3-pointers. | BadAt(jack, midRangeShot) ∧ GoodAt(jack, twos) → ¬GoodAt(jack, twos) ∧ GoodAt(jack, threes) |
If Jack is solid at shooting 2-pointers or successfully shoots a high percentage of 3-pointers, then Jack struggles at half court shots and is bad at mid-range shots. | GoodAt(jack, twos) ∨ GoodAt(jack, threes) → BadAt(jack, halfCourtShot) ∧ BadAt(jack, midRangeShot) |
No plants are fungi. | ∀x (Plant(x) → ¬Fungi(x)) |
Mushrooms are fungi. | ∀x (Mushroom(x) → Fungi(x)) |
No plants are mushrooms. | ∀x (Plant(x) → ¬Mushroom(x)) |
No road is dustless. | ∀x (Road(x) → ¬Dustless(x)) |
Some streets are roads. | ∃x ∃y (Street(x) ∧ Street(y) ∧ Road(x) ∧ Road(y) ∧ ¬(x=y)) |
Some streets are dustless. | ∃x ∃y (Street(x) ∧ Street(y) ∧ Dustless(x) ∧ Dustless(y) ∧ ¬(x=y)) |
New York City is located on the East Coast. | LocatedOn(newYorkCity, eastCoast) |
Seattle is located on the West Coast. | LocatedOn(seattle, westCoast) |
If a person is somewhere located on the East coast and is traveling to somewhere located on the west coast, they will be on a long flight. | ∀x ∀y ∀z ((TravelingFrom(x, y) ∧ LocatedOn(y, eastcoast) ∧ TravelingTo(x, z) ∧ LocatedOn(z, westcoast)) → OnLongFlight(x)) |
People in business class from New York City to Seattle are not in first class. | ∀x (InBuisnessClass(x) ∧ TravelingTo(x, seattle) ∧ TravelingFrom(x, newYorkCity) → ¬InFirstClass(x)) |
People on long flights are uncomfortable unless they're in first class. | ∀x (OnLongFlight(x) ∧ ¬InFirstClass(x) → Uncomfortable(x)) |
People traveling in business class from New York City to Seattle will be uncomfortable. | ∃x (TravelingTo(x, seattle) ∧ TravelingFrom(x, newYorkCity) ∧ uncomfortable(x)) |
Musicians have very busy lives. | ∀x (Musician(x) → Have(x, busyLife)) |
Singh Kaur is a musician and famous. | Musician(singhKaur) ∧ Famous(singhKaur) |
If a musician is not famous, that musician will not make a lot of money. | ∀x (Musician(x) ∧ ¬Famous(x) → ¬MakeALotOfMoney(x)) |
A musician can be a singer or a writer. | ∃x (Musician(x) ∧ (Singer(x) ∨ Writer(x))) |
Singh Kaur makes a lot of money. | MakeALotOfMoney(singhKaur) |
Singh Kaur is a writer. | Writer(singhKaur) |
Singh Kaur has a very busy life. | Have(singhKaur, busyLife) |
Each building is tall. | ∀x (Building(x) → Tall(x)) |
Everything tall has height. | ∀x (Tall(x) → Height(x)) |
All buildings are magnificent. | ∀x (Building(x) → Magnificent(x)) |
A cat named Garfield, the main character of the film Garfield, is orange and fat and likes having lasagna. | Cat(garfield) ∧ MainCharacterOf(garfield, filmGarfield) ∧ Orange(garfield) ∧ Fat(garfield) ∧ Like(garfield, lasagna) |
Garfield shares a home with Odie, another pet of Jon's. | PetOf(garfield, jon) ∧ PetOf(odie, jon) ∧ ShareHomeWith(garfield, odie) |
Garfield hates Odie. | Hate(garfield, odie) |
A pet who hates the pet with whom he shares the same owner is childish and possessive. | ∀x ∀y ∃z (PetOf(x, z) ∧ PetOf(y, z) ∧ Hate(x, y) → Childish(x) ∧ Possessive(x)) |
The main character of the film Garfield is childish and possessive. | ∃x (MainCharacterOf(x, garfield) ∧ Childish(x) ∧ Possessive(x)) |
All humans are capable of abstract thoughts. | ∀x (Human(x) → CapableOf(x, abstractThought)) |
Plants are not capable of abstract thoughts. | ∀x (Plant(x) → ¬CapableOf(x, abstractThought)) |
All multicellular creatures that are autotrophic or digest food internally are plants and animals. | ∀x (MulticellularCreature(x) ∧ (Autotrophic(x) ∨ DigestFoodInternally (x)) → Plant(x) ⊕ Animal(x)) |
All goats are animals. | ∀x (Goat(x) → Animal(x)) |
Dirt is not an animal. | ∀x (Dirt(x) → ¬Animal(x)) |
Hulu is a goat or a human. | Goat(hulu) ∨ HumanBeing(hulu) |
Hulu is a multicellular creature that is autotrophic or digests food internally. | (MulticellularCreature(hulu) ∧ (Autotrophic(hulu) ∨ DigestFoodInternally (hulu)) |
Hulu is capable of abstract thoughts. | CapableOf(hulu, abstractThought) |
Hulu is not capable of abstract thoughts. | ¬CapableOf(hulu, abstractThought) |
Hulu is dirt. | Dirt(hulu) |
Hulu is an animal or dirt. | Animal(hulu) ∨ Dirt(hulu) |
Hulu is either an animal or dirt, but not both. | Animal(hulu) ⊕ Dirt(hulu) |
If Hulu is either an animal or dirt, then Hulu is capable of abstract thoughts and is dirt. | Animal(hulu) ⊕ Dirt(hulu) → CapableOf(hulu, abstractThought) ∧ Dirt(hulu) |
A controlled substance is a drug. | ∀x (ControlledSubstances(x) → Drugs(x)) |
There exist both harmful and beneficial controlled substances. | ∃x ∃y (ControlledSubstances(x) ∧ ControlledSubstances(y) ∧ (¬(x=y)) ∧ Beneficial(x) ∧ Harmful(y)) |
If a child is exposed to a controlled substance, they are in chemical endangerment. | ∀x ∀y ((Child(x) ∧ ControlledSubstances(y) ∧ ExposedTo(x, y)) → InChemicalEndangerment(x)) |
Chemical Endangerment is harmful. | ∀x (InChemicalEndangerment(x) → Harmful(x)) |
The Controlled Substances Act was an act passed in 1971. | PassedIn(controlledSubstancesAct, yr1971) ∧ Act(controlledSubstancesAct) |
Some Acts prevent harmful things. | ∃x ∃y(Act(x) ∧ PreventsHarm(x) ∧ (¬(x=y)) ∧ Act(y) ∧ PreventsHarm(y)) |
The Controlled Substances Act prevents harmful things. | PreventsHarm(controlledSubstancesAct) |
Some drugs are beneficial. | ∃x ∃y(Drugs(x) ∧ Beneficial(x) ∧ (¬(x=y)) ∧ Drugs(y) ∧ Beneficial(y)) |
A child in chemical endangerment is in harm. | ∀x ((Child(x) ∧ InChemicalEndangerment(x)) → Harmful(x)) |
No people who have corporate jobs are taking more than normal financial risks. | ∀x (Have(x, corporateJob) → ¬Take(x, financialRisk)) |
All entrepreneurs are taking more than normal financial risks. | ∀x (Entrepreneur(x) → Take(x, financialRisk)) |
All risk-averse working people are people who have corporate jobs. | ∀x (RiskAverse(x) → Have(x, corporateJob)) |
All working people who hate working for others want to be entrepreneurs. | ∀x (∃y ∃z (¬(y=x) ∧ ¬(z=x) ∧ ¬(y=z) ∧ HateWorkingFor(x, y) ∧ HateWorkingFor(x, z)) → Entrepreneur(x)) |
If Mark Zuckerberg is neither an entrepreneur nor a person who hates working for others, then Mark Zuckerberg is not a risk-averse working person. | ¬Entrepreneur(markZuckerberg) ∧ ¬(∃y ∃z (¬(y=markZuckerberg) ∧ ¬(z=markZuckerberg) ∧ ¬(y=z) ∧ HateWorkingFor(markZuckerberg, y) ∧ HateWorkingFor(markZuckerberg, z))) → ¬RiskAverse(markZuckerberg) |
Mark Zuckerberg is an entrepreneur. | Entrepreneur(markZuckerberg) |
Mark Zuckerberg is a risk-averse person. | RiskAverse(markZuckerberg) |
Mark Zuckerberg is not a risk-averse person. | ¬RiskAverse(markZuckerberg) |
Wildfeed exists as an unannounced program. | ∃x (Wildfeed(x) ∧ Unannounced(x) ∧ Program(x)) |
Wildfeed can be sporting events, news, or syndicated shows. | ∀x (Wildfeed(x) → SportingEvent(x) ∨ News(x) ∨ SyndicatedShow(x)) |
Pre-recorded content is a copyright violation. | ∀x (Prerecorded(x) → CopyrightViolation(x)) |
Programs are pre-recorded. | ∀x (Program(x) → Prerecorded(x)) |
Some wildfeed is violating copyright laws. | ∃x (Wildfeed(x) ∧ CopyrightViolation(x)) |
Wildfeed can be prerecorded. | ∃x (Wildfeed(x) ∧ Prerecorded(x)) |
Syndicated shows are copyright violations. | ∃x (SyndicatedShows(x) ∧ CopyrightViolation(x)) |
New York City is Located in the United States of America. | LocatedIn(newYorkCity, unitedStatesOfAmerica) |
The United States of America is part of North America. | LocatedIn(usa, northAmerica) |
North America is in the western hemisphere of the earth. | LocatedIn(northAmerica, westernHemisphere) |
New York City is a highly developed city. | HighlyDeveloped(newYorkCity) |
If place A is located in place B and place B is located in place C, then place A is located in place C. | ∀x ∀y ∀z ((LocatedIn(x, y) ∧ LocatedIn(y, z)) → LocatedIn(x, z)) |
A highly developed city is located in the western hemisphere of the earth. | ∃x (HighlyDeveloped(x) ∧ LocatedIn(x, westernHemisphere)) |
The United States of America is not located in the western hemisphere of the earth. | ¬LocatedIn(unitedStatesOfAmerica, westHemisphere) |
New York City is located in New York State. | LocatedIn(newYorkCity, newYork) |
Catullus 4 is a poem written by the ancient Roman writer Catullus. | Poem(catullus4) ∧ WrittenBy(catullus4, catullus) ∧ AncientRomanWriter(catullus) |
Catullus 4 is a story about the retirement of a well-traveled ship. | Story(catullus4) ∧ About(catullus4, retirementOfAWellTraveledShip) |