TRƯỜNG ĐẠI HỌC BÁCH KHOA TP.HCM Khoa Khoa học & Kỹ thuật Máy tính Artificial Intelligence (Spring 2016) Tutorial Question Given the following symbols: m 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 co a Emily is either a surgeon or a lawyer e Use these symbols to write the following assertions in first-order logic: c All surgeons are doctors nZ d Joe does not have a lawyer on b Joe is an actor, but he also holds another job e Emily has a boss who is a lawyer f There exists a lawyer all of whose customers are doctors Question nh V ie g Every surgeon has a lawyer Si 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 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) SinhVienZone.com https://fb.com/sinhvienzonevn TRƯỜNG ĐẠI HỌC BÁCH KHOA TP.HCM Khoa Khoa học & Kỹ thuật Máy tính Question 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 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 m (Note: you not need any additional axioms.) Question co 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” Q1 What did Mary go shopping for? on e Represent this information by predicate logic sentences in such a way that you can solve questions below: nZ Q2 What did Mary find that she liked and what was its color? Si nh V ie Q3 Did Mary buy anything? SinhVienZone.com https://fb.com/sinhvienzonevn