08-LogicalArgs

08-LogicalArgs - Discussion#8 Chapter 1 Sections 1-3 1...

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Unformatted text preview: Discussion #8 Chapter 1, Sections 1-3 1 Discussion #8 Introduction to Logic and Logical Arguments Discussion #8 Chapter 1, Sections 1-3 2 Topics Introduction to logic and logical arguments Propositions Connectives Propositional expressions Logic is used for: Databases Software specification Program validation Computer hardware design Semantic web … And yes … Projects for CS236 Discussion #8 Chapter 1, Sections 1-3 3 Logical Arguments Consider the following statements. 1. if you study then you succeed 2. you study 3. you succeed These three statements create a logical argument. Lines 1 and 2 are premises and line 3 is the conclusion. This logical argument is sound. Premises can be true or false. If the premises are true, the conclusion must be true. If one (or more than one) of the premises is false, the argument is still sound, but we don’t know whether the conclusion is true or false. Discussion #8 Chapter 1, Sections 1-3 4 Modus Ponens if you study then you succeed you study you succeed Aristotle called this modus ponens: if P then Q P Q Premises Conclusion (a rule of inference – one of the most important rules) Discussion #8 Chapter 1, Sections 1-3 5 Important! We are dealing with the validity of an argument, NOT with the validity of the result! In logic, it doesn’t matter if a logical statement makes sense or not. What does matter is that if the premises are correct, then so is the result. Discussion #8 Chapter 1, Sections 1-3 6 Modus Ponens Examples P: I study hard Q: I get an A P: cows give milk Q: doors open P: I follow the gospel plan Q: I will be exalted P: you sail past the end of the world Q: you will fall off Makes sense Doesn’t make sense Makes sense Doesn’t make sense if P then Q P Q Discussion #8 Chapter 1, Sections 1-3...
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This note was uploaded on 03/02/2012 for the course C S 236 taught by Professor Michaelgoodrich during the Winter '12 term at BYU.

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08-LogicalArgs - Discussion#8 Chapter 1 Sections 1-3 1...

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