Download to read offline
Logic_of_Informatics_-_Rules_of_Inference.pptx
- 1. Logic of Informatics Rulesof Inference
- 2. Last Lecture • Converse •Inverse • Contrapositive • Tautology • Contradiction
- 3. What is anargument? An argument is a sequence of statements or premises that end in a conclusion. Ex: If I jump I will fall I jump Therefore, I will fall q p q p This argument has the form:
- 4. Another Example Ex: Premise: IfI eat too much, my stomach will be hurt Premise: My stomach doesn’t hurt Conclusion: Therefore, I don’t eat too much p q This argument has the form: p q q p
- 5. The purpose ofrules of inference We use rules of inference to construct valid arguments. A valid argument is one in which it is not possible for the conclusion to be false if the premises are true. The argument is valid iff the truth of all premises implies the conclusion is true
- 6. How to determinethe validity of argument? The argument form with premises q p p p n ) ( 2 1 and conclusion q is valid when n p p p , , , 2 1 is a tautology
- 7. The Rules ofInference - Modus Ponens q p q p If I am late, my teacher is angry to me I am late Therefore, my teacher is angry to me
- 8. The Rules ofInference - Modus Tollens p q q p If grass is blue, then trees are blue Trees are not blue Therefore, grass is not blue
- 9. The Rules ofInference - Hypothetical Syllogism p q q r p r If today is raining, then we are late If we are late, then our teacher will be angry Therefore, if today is raining then our teacher will be angry
- 10. The Rules ofInference - Disjunctive Syllogism p q q p p q p q OR My wallet is in my pocket or left behind at home No wallet in my pocket Therefore, my wallet left behind at home
- 11. The Rules ofInference - Conjunction p q p q He takes Discrete Mathematics Lecture He repeats Algorithms Lecture Therefore, he takes Discrete Mathematics and repeats Algorithms
- 12. The Rules ofInference - Addition p p q q p q OR 𝑝 = I like tea, 𝑞 = I like coffee I like tea Therefore, I like tea or coffee
- 13. The Rules ofInference - Simplification p q p p q q OR I am clever in mathematic and computer science Therefore, I am clever in mathematic
- 14. The Rules ofInference - Dilemma p q p r q r r Either we increase the price or we decrease the quality. If we increase the price, sales will slump. If we decrease the quality, sales will slump. Therefore, sales will slump.
- 15. Exercise 1 • Determinewhether the following argument is valid / Invalid a). P (Q R) R P Q b). P (Q R) Q (P R) P R
- 16. Exercise 2 One day,you want to go to college and realized that you do not wear glasses. Having to remember, there are some facts that you make sure the truth: 1. If the glasses are on the kitchen table, then I would have seen it as breakfast. 2. I read the newspaper in the living room or I read it in the kitchen. 3. If I read the newspaper in the living room, then surely put my glasses on the coffee table. 4. I do not see my glasses at breakfast time. 5. If I read a book in bed, then put my glasses on the bedside table. 6. If I read the newspaper in the kitchen, then my glasses are on the kitchen table. Based on these facts, prove / show that the glasses left on the coffee table! p q r s r t q u w s p
- 17. Exercise 3 • Provethe validity of the following arguments using the rules of inference! p q (p q) r r