CS 416
Artificial Intelligence
Fall 2004

 

Homework 1: Chapters 8 and 9 in Russell & Norvig
Due: October 20th at Class (5:00)


  1. Modified from 8.7 on page 269: Represent the sentence “All Germans speak the same languages” in predicate calculus. Use Speaks(x,l), meaning that person x speaks language l, and German(y), meaning that y is a German person.


  1. What axiom is needed to infer the fact Sister(Laura, Jim) given the facts Male(Jim), Female(Laura), Father(John, Jim), Father(John, Laura), Mother(Luann, Laura), and Mother(Luann, Jim)? (Jim, John, Laura, and Luann are constants)


  1. Modified from 8.10 on page 269: Rewrite the propositional Wumpus world facts from Section 7.7 into first-order logic. You will want to read all of chapter 7, if you have not already done so, in order to understand the complexity of the Wumpus world using propositional logic.


  1. Modified from 9.4 on page 316: For each pair of atomic sentences, give the most general unifier if it exists: (a, b, x, y, and z are variables)

    1. P(a,b,b), P(x, y, z).

    2. Q(y, G(a, b)), Q(G(x, x), y).

    3. Older(Father(y), y), Older(Father(x), John).

    4. Knows(Father(y), y), Knows(x, x).


  1. 9.17 on page 318: How can resolution be used to show that a sentence is valid? Unsatisfiable?