First-Order Logic Quiz

What is the main limitation of Propositional Logic?

• Can't represent patterns or regularities

• Can't directly talk about properties of individuals or relations between individuals

• Can identify individuals like Mary or 3

• Can represent generalizations easily

What does First-Order Logic add to Propositional Logic?

• Connectives and quantifiers

• Only quantifiers

• Only variables

• Relations, variables, and quantifiers

How can the sentence 'Every elephant is gray' be represented in First-Order Logic?

• ∃x (elephant(x) ^ gray(x))

• ∀x (elephant(X) ^ white(X))

• ∀x (elephant(x) ^gray(x))

• ∃x (elephant(x) ^gray(x))

What is the purpose of skolem constant in Existential instantiation?

• To replace the variable with a new constant not occurring in the KB

• To replace the variable with a new variable symbol

• To replace the variable with any constant in the KB

• To replace the variable with a constant symbol

Which quantified inference rule allows inferring P(c) from (x) P(x)?

• Existential generalization

• Universal generalization

• Existential instantiation

• Universal instantiation

What is the correct translation of 'All purple mushrooms are poisonous' to First-Order Logic?

• ∀x (mushroom(x) ^purple(x)) →poisonous(x)

• ∀x purple(x) ^mushroom(x) →poisonous(x)

• ∃x (mushroom(x) ∃purple(x)) →∃poisonous(x)

• ∃x ∃y mushroom(x) purple(x) mushroom(y) purple(y) ^ (x=y) z (mushroom(z) purple(z)) →((x=z) (y=z))

What is the correct translation of 'There are exactly two purple mushrooms' to First-Order Logic?

• ∃x ∃y mushroom(x) ^purple(x) ^mushroom(y) ^purple(y) ^ (x=y) ^ ∀z (mushroom(z) ^purple(z)) →((x=z) v (y=z))

• ∀x ∀y mushroom(x) ^purple(x) ^mushroom(y) purple(y) ^ (x=y) ∃z (mushroom(z) ^purple(z)) →((x=z) (y=z))

• ∀x ∀y mushroom(x) purple(x) ^mushroom(y) v purple(y) ^ (x=y) ∃z (mushroom(z) ^purple(z)) →((x=z) (y=z))

• ∃x ∃y mushroom(x) ^ purple(x) v mushroom(y) v purple(y) ^(x=y) v z (mushroom(z) v purple(z)) →((x=z) (y=z))

What is the correct translation of 'You can fool some of the people all of the time' to First-Order Logic?

• ∃x ∀t person(x) ∧ time(t) →can-fool(x,t)

• ∀x ∃t person(x) ∧ time(t) →can-fool(x,t)

• ∃x ∃t person(x) ∧ time(t) →can-fool(x,t)

• ∀x ∀t person(x) ∧ time(t) →can-fool(x,t)

What is the correct translation of 'You can fool all of the people some of the time' to First-Order Logic?

• ∀x ∃t (person(x) →time(t) ∧ can-fool(x,t))

• ∃x ∀t person(x) time(t) →can-fool(x,t)

• ∀x ∀t person(x) time(t) →can-fool(x,t)

• ∃x ∃t person(x) time(t) →can-fool(x,t)

What is the correct translation of 'No purple mushroom is poisonous' to First-Order Logic?

• ∃x ∃y mushroom(x) ^purple(x) ^mushroom(y) ^purple(y) ^ (x=y) z (mushroom(z) ^purple(z)) →((x=z) (y=z))

• ∃x (mushroom(x) ^purple(x)) →^poisonous(x)

• ~ ∃ x purple(x) ^ mushroom(x) ^poisonous(x)

• ∀x ∀y mushroom(x) ^purple(x) ^mushroom(y) ∀ purple(y) ^(x=y) ^z (mushroom(z) ^purple(z)) →((x=z) (y=z))