Artificial Intelligence 2
<A href="../syllabus.html"> <IMG SRC="../gr_u_arr.gif"></A> <h2>Logic Homework</h2> <font size=+2> <p>Do the following two problems below (they are from the text) and email me your answers: <ul> <li>Problem 8.9 (page 316) parts a through d. You can try part e for extra credit. <br><br> <li>Problem 8.10 (page 317) parts a through c. </ul> <br><br> <p><b>Problem 8.9:</b> <br><br> This exercise uses the function <i>MapColor (x)</i> and predicates <i>In (x,y), Borders (x,y)</i>, and <i>Country (x)</i>, whose arguments are geographical regions, along with constant symbols for various regions. In each of the following we give an English sentence and a number of candidate logical expressions. For each of the following expressions, state whether it <ol> <li>correctly expresses the English sentence; <li>is syntactically invalid and therefore meaningless; or <li>is syntactically valid but does not express the meaning of the English sentence. </ol> <br> <img src="Exercise8_9.jpg" width=1000> <br><br> <b>Problem 8.10:</b> <br><br> <p>Consider a vocabulary with the following symbols: <ul> <p>Occupation(p,o): A predicate that means that Person p has occupation o. <p>Customer(p1,p2): A predicate that means that Person p1 is a customer of Person p2. <p>Boss(p1,p2): A predicate that means that Person p1 is a boss of Person p2. <p>Doctor, Surgeon, Teacher, Lawyer, Actor: Constants that denote occupations. <p>Emily, Joe: Constants that denote Persons. </ul> <p>Use these symbols to write the assertions in parts a through g in first order logic. Here are a few examples: <ul> <p>Occupation(Paul,Teacher) means "Paul is a Teacher." <p>Boss(Dino,Paul) means "Dino is a boss of Paul." <p>Occupation(Bob,Lawyer) ∧ Occupation(Bob,Teacher) means "Bob is a Lawyer and a Teacher." <p>∀x Occupation(x,Teacher) ⇒ Occupation(x,Actor) means "Every teacher is an actor." </ul> <p>Now the homework: <ul> <p>a. Emily is either a surgeon or a lawyer. <p>b. Joe is an actor, but he also holds another job. <p>c. All surgeons are doctors. <p>d. Joe does not have a lawyer (meaning that he is not a customer of any lawyer.) <p>e. Emily has a boss who is a lawyer. <p>f. There exists a lawyer all of whose customers are doctors. <p>g. Every surgeon has a lawyer. </ul> </font>