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TRƯỜNG ĐẠI HỌC BÁCH KHOA TP.HCM Khoa Khoa học & Kỹ thuật Máy tính Artificial Intelligence Spring 2016 Tutorial 5 Question 1..  Doctor, Surgeon, Lawyer, Actor: Constants denoting occu

TRƯỜNG ĐẠI HỌC BÁCH KHOA TP.HCM

Khoa Khoa học & Kỹ thuật Máy tính

Artificial Intelligence (Spring 2016)

Tutorial 5

Question 1

Given the following symbols:

 Occupation(p, o) : Predicate Person p has occupation o

 Customer(p1,p2): Predicate Person p1 is a customer of person p2

 Boss(p1,p2): Predicate Person p1 is a boss of person p2

 Doctor, Surgeon, Lawyer, Actor: Constants denoting occupations

 Emily, Joe: Constants denoting people

Use these symbols to write the following assertions in first-order logic:

a Emily is either a surgeon or a lawyer

b Joe is an actor, but he also holds another job

c All surgeons are doctors

d Joe does not have a lawyer

e Emily has a boss who is a lawyer

f There exists a lawyer all of whose customers are doctors

g Every surgeon has a lawyer

Question 2

2.1 Does the fact ¬Spouse(George, Laura) follow from the facts Jim ≠ George and Spouse(Jim,

Laura)? If so, give a proof; if not, supply additional axioms as needed What happens if we use Spouse as a unary function symbol instead of a binary predicate?

2.2 Explain what is wrong with the following proposed definition of the set membership

predicate ∈ :

∀ x, s x ∈ {x|s}

∀ x, s x ∈ s ⇒ ∀ y x ∈ {y|s}

Question 3 For each pair of atomic sentences, give the most general unifier if it exists:

a P(A, B, B), P(x, y, z)

b Q(y, G(A, B)), Q(G(x, x), y)

c Older(Father(y), y), Older(Father(x), John)

d Knows(Father(y), y), Knows(x, x)

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TRƯỜNG ĐẠI HỌC BÁCH KHOA TP.HCM

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Question 4 Let L be the first-order language with a single predicate S(p, q), meaning “p shaves q.” Assume a domain of people

a Consider the sentence “There exists a person P who shaves everyone who does not shave themselves, and only people that do not shave themselves.” Express this in L

b Convert the sentence in (a) to clausal form

c Construct a resolution proof to show that the clauses in (b) are inherently inconsistent (Note: you do not need any additional axioms.)

Question 5

We have a story: “Mary went shopping for a new coat She found a red one she really liked

When she got it home, she discovered that it went perfectly with her favorite dress”

Represent this information by predicate logic sentences in such a way that you can solve questions below:

Q1 What did Mary go shopping for?

Q2 What did Mary find that she liked and what was its color?

Q3 Did Mary buy anything?

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