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Unformatted text preview: CPSC 121 Lecture 8 January 21, 2009 Menu January 21, 2009 Topics: Summary of Learning Goals (Epp Chapter 1) Predicates and Quantified Statements Reading: Today: Epp 2.1 Next: Epp 2.22.4 Reminders: On-line Quiz 5 deadline 9:00pm January 22 Assignment 1 due Friday, January 30, 17:00 In-class Quiz 1 Wednesday, February 4 Midterm exam Tuesday, February 24 (evening) READ the WebCT Vista course announcements board Important Take Away Point from Last Lecture Formal logic is less concerned with the question, What are the right hypotheses to make? than it is with the question, Given a set of hypotheses, what are the logical consequences of those hypotheses? Of course, we want to use formal logic to prove things about the computer circuits we design and build. We do care that our hypotheses correctly represent the theory we intend our circuits to implement In this course, the focus is on the connection between formal logic and the computer circuits we design and build. More generally, in computer science, we also are concerned about the connection between formal logic and the programming languages we design and implement (and the programs we subsequently write). We do care that our hypotheses correctly represent the algorithms we intend our programs to implement. Heres the example from geometry mentioned verbally during the previous lecture. An Example from Geometry In 2-D Euclidean Geometry (i.e., plane geometry) we know that two parallel lines never meet Question: Can you prove this? Answer: No. This is an hypothesis (i.e., an axiom) of Euclidean geometry Question: What happens if you throw this axiom away? Answer: You get different (and interesting) geometries. One example is spherical geometry (i.e., geometry on the surface of a sphere) where, in fact, parallel lines do meet To illustrate, imagine two people on the earths equator, one in South America and the other in Africa. They both head due north. At that moment they are headed in parallel directions (i.e., due north). If they were to continue, their paths would eventually cross at the north pole. The geometry of the plane is fundamentally different from the geometry of the sphere, something that has made map-making (i.e., cartography) a challenge for centuries....
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- Spring '08