01-intro

01-intro - Welcome to CS 245 Instructor: Brad Lushman Web...

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Welcome to CS 245 Instructor: Brad Lushman Web page: http://www.student.cs.uwaterloo.ca/˜cs245 Read everything on the Web page carefully as soon as possible, especially the academic offenses page. Newsgroup: uw.cs.cs245 Read the newsgroup at least daily for fast-breaking items and discussions of common interest. 1
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Course logistics Assignments (six to eight in total) will be worth roughly 25%, the midterm 25%, and the final exam 50%. One or more graduate student TAs will be delivering weekly tutorials, with some reinforcement of lecture material and some practice in solving problems. 2
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The required textbook is “Logic in computer science: modelling and reasoning about systems” (second edition), by Michael Huth and Mark Ryan. The bookstore currently has copies of a book by Nissanke on its shelves. We will not be using this text. The Huth and Ryan book has been ordered. We will use Chapters 1, 2, and 4 (out of 6). If time permits, we will look at some of the other relevant topics in the book. 3
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Overview of course This course is about formal mathematical logic and its application to computer science. In your previous CS and math courses, you have been exposed to some aspects of logic, in varying degrees of formality. Math 135 introduced you to varying styles of mathematical proof using the topic of elementary number theory. 4
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But what is logic? 5
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A timeless question. .. UW Motto: Concordia cum veritate WLU Motto: Veritas omnia vincit Quid est veritas? 6
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Quid est veritas — What is truth? What is “truth”? More concretely, let S be a statement. What do we mean when we say that S is “true”? 7
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One possible answer S is true if S can be obtained from some established “basic truths” by some established “truth derivation procedure”. This is “syntactic truth” or derivability. 8
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Example for any x , x = x is a basic truth for any x , y , z , if x = y is true, then z + x = y + z is true Then “john = john” is true and “mary + john = john + mary” is true, and “john + mary = john + mary” is true, but “john + mary + ted = mary + john + ted” is not true. Clearly, this setup does not capture all that we believe to be “true”, but maybe with the right set of basic truths, and the right derivation procedure. ... 9
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Every statement S is either an atomic statement (which may or may not be a basic truth) or a pair of statements S 1 and S 2 , joined by some connective 2 . Let B be the set { T,F } . To each connective 2 associate a function meaning( 2 ) : B × B B . An interpretation is a function φ that maps each atomic statement to either T or F , and such that Φ( S 1 2 S 2 ) = (meaning( 2 ))( φ ( S 1 ) ( S 2 )) . Then
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01-intro - Welcome to CS 245 Instructor: Brad Lushman Web...

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