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