SEG45630 Computational Intelligence for Decision Making (2008-09 Second Term) Assignment 2 (100 points) Due time and date: 7pm, March 23 Monday Submit to assignment box D03, 5/F ERB Submission Requirements The hand-in version must be ordered correctly and stapled in the top left corner. The hand-in version must include a header page (or with sufficient space) indicating: student name, student ID and assignment number. Question 1. Decide whether each of the following sentences is valid, satisfiable, or neither. Please first use equivalence rules to rewrite the sentences into some simpler forms and then construct a truth table over the symbols to evaluate the truth of the sentences. [20pts] (1) ( Smoke Fire ) (( Smoke Heat ) Fire ) (2) Big Dumb ( Big Dumb) Question 2. Given the following, can you prove that the unicorn is mythical? How about magic? Horned? Please use propositional logic to express each point in the following paragraph. Answer the above questions based on the sentences you write. [20pts] If the unicorn is mythical, then it is immortal; but if it is not mythical, then it is a mortal mammal. If the unicorn is either immortal or a mammal, then it is horned. The unicorn is magical if it is horned. Question 3. Represent the following sentences in first-order logic [20pts] (a) Politicians can fool some persons all of the time, and they can fool all persons some of the time, but they cannot fool all persons all of the time. Using predicates: Politician(x) and Person(x) and Relation: Fools(x, y, t) means x fools y at time t. (b) Every person who buys a policy is smart. Using predicates: Person(x), Policy(x), Smart(x) and Relation: Buys(x,y) means x buys y. Question 4. [Chapter 9]Write down logical representations for the following sentences, suitable for use with Generalized Modus Ponens: a. b. c. d. e. f. Horses, cows and pigs are mammals. An offspring of a horse is a horse. Bluebeard is a horse. Bluebeard is Charlie’s parent. Offspring and parent are inverse relations. Every mammal has a parent. Then draw the proof tree generated by the backward-chaining algorithm for the query h, Horse (h) , where clauses are matched in the order given in your logical rules. [20pts] Question 5. [Chapter 9] [20pts] From “Horses are animals,” it follows that “The head of a horse is the head of an animal.” Demonstrate that this inference is valid by carrying out the following steps: a. Translate the premise and the conclusion into the language of first-order logic. Use three predicates: HeadOf(h,x) (meaning “h is the head of x”), Horse(x), and Animal(x). b. Negate the conclusion and convert the premise and the negated conclusion into conjunctive normal form. c. Use resolution to show that the conclusion follows from the premise.