※ 本文是否可提供台大同学转作其他非营利用途？（须保留原作者 ID） （是／否／其他条件）：是 哪一学年度修课： 107-2 ψ 授课教师 (若为多人合授请写开课教师，以方便收录) 陈伟松 λ 开课系所与授课对象 (是否为必修或通识课 / 内容是否与某些背景相关) 资工所选修 δ 课程大概内容 摘自课程网： Lesson 1. Preliminaries Lesson 2. Compactness theorem for propositional calculus Lesson 3. Proof system in propositional calculus Lesson 4. Completeness of propositional calculus Lesson 5. First-order logic (FO) part I Lesson 6. First-order logic (FO) part II Lesson 7. Logical consequences and theories Lesson 8. Proof system in FO Lesson 9. Gödel's completeness theorem Lesson 10. Löwenheim-Skolem theorem and categorical sets Lesson 11. Gödel's incompleteness theorem part. I Lesson 12. Gödel's incompleteness theorem part. II Lesson 13. Decision problems in FO Lesson 14. Some topics in logic in computer science Ω 私心推荐指数(以五分计) ★★★★★ ★★★★★ η 上课用书(影印讲义或是指定教科书) 课程网上会有每章讲议，老师也是看着它教课。 μ 上课方式(投影片、团体讨论、老师教学风格) 老师板书，英文授课，板书大概是我戴了眼镜感觉像没戴一样XD 基本上就是有条有理的把定义、推导做一遍，曾课上着就说应该叫大家自己看。 遇到同学表示不懂或看起来不懂的地方就会停下来或重新再讲一次。 时常会喷出有趣的话，例如： 2019.2.18 Course Info Who likes 2:20? (silent) No one likes 2:20. Let's make it 2:30. (laughter) Or 2:00? 2:00 is even better, I can go home earlier. 2019.2.18 Course Info No course on April first. Okay everyone is happy. 2019.2.18 Space I will give you a format for your homework. If you want to write by hand, you can print it out, I will give you space. If you use more than the space, then your answer is wrong. 2019.2.18 Know something by hard You know how to know something by hard right? Suppose somebody wakes you up at midnight, "what is countable sets?", "Let N be the set of natural numbers......" something like that Okay? 2019.2.25 Logical consequences If you want to show this and don't know how to show this, show this. If you want to show this and don't know how to show this, show this. If you want to show this and don't know how to show both, well, good luck. If you don't know how to show both, then, ask your friend. 2019.3.4 Proof Sometimes I write a proof, I think it's a good proof and I submit it to my teacher. But the teacher says that this is not a proof it is nonsense. And my friend who wrote something that I think is nonsense, got full credits. This always happens, what is a proof? 2019.3.4 ~(a * ~b) What is your reaction to this? If you write this in your homework my reaction is "I want to mark this wrong," so I don't need to read it. 2019.3.4 Experts Some experts are very expert. They think that everything is the same. 2019.3.3 Homework Being a teacher is good if you don't know, then homework! 2019.3.11 Claim If you don't know how to prove, write "claim". Though you don't know how to prove at least you write something, and you feel confident. 2019.3.11 Computer science Maybe someday you are super smart and learn some sophisticated mathematics. It might say something would be true only with the axiom of choice. For me, I stop at countable. But this is okay, for computer science. Okay, all that we have done is good. We have used sophisticated things as Zorn's lemma. 2019.3.18 Philosopher's talk Who has class on Friday? It's okay if you have class on Friday. But in May, May 10. There will be a talk about logic, at 104. A philosopher, I don't know philosophers, but I am hosting the talk. It's about logic. 2019.3.18 VAR VAR stands for "variable". If you watch football VAR stands for Video Assistant Referee. 2019.3.18 Definition For this week and next week, there are no theorems only definitions. Two years ago, someone said that logic is boring, there are only definitions. What can I do about that? 2019.3.25 Equi-satisfiable This his hard. (?) Because it is a trick. (?) Well, in computer science it is useless. How can you introduce a function? 2019.3.25 Wake-up I suppose you take this course because you are interested, so I tell you a story to wake you up. 2019.4.8 Embarrass Just to make sure you know because if you pass this class and someone asks you and you don't know. It is embarrassing, for me. 2019.4.8 Incompleteness Completeness theorem is for proof systems, Incompleteness theorem is for theories. Even if you don't understand, you can show off to your friend. 2019.4.15 Proof system These five rules are rules of propositional logic. We use it in our everyday, proof, not everyday life. Maybe everyday life. 2019.4.15 Hard Who finds the homework hard? (someone raises its hand) Ah~ someone finds it hard, is the English hard? Or the logic hard? 2019.4.15 Grow a tree When you take linear algebra, you don't grow a tree. 2019.4.15 Logician Logicians like this kind of proof, everything is from definitions. Frankly speaking, I like this kind of proof. 2019.4.29 Nothing The course itself contains nothing. Not nothing, everything is elementary 2019.4.29 Alaph Alaph is Hebrew, in Hebrew, they write from right to left like ancient Chinese. Why, because in the old-time people write with a hammer, and our right hand is stronger. Today, we write with ink, so we write from left to right. Some history. 2019.4.29 Alphabet In Greek, we have alpha, beta ..., that's why we have "alphabet". Some history. I know a little more than logic. 2019.4.29 Y Y = Z union Gamma, Why is Y satisfiable? Maybe not Y, Z. 2019.4.29 Skolem paradox It is called a paradox because it looks like a paradox. 2019.5.13 Program The program here can be C++, your favorite language, (?), or Java or Python. 2019.5.13 Assumptions Sometimes you come to me and say "why my proof is not a proof and his proof is a proof". I'd say maybe you use different assumptions. When you can't prove something, you assume it. Mathematicians do this too. And Godel says that there is always something you have to assume. 2019.5.13 Incompleteness This is Godel's Incompleteness Theorem. No Theory of everything, no bible ... For us, as a CS student, it means what it says, no philosophy meanings. 2019.5.13 Computers A long long time ago, what do we have? Maybe we have stones. Okay, a long long time ago, we don't have computers, but we want to build computers. 2019.5.20 Delicate Step 1, is technical, and Step 2, is delicate. You know delicate, it's short but it's confusing. 2019.5.20 ? student: What is the intuitive meaning of Beta and gamma? What can I say? well, it takes time. 2019.5.20 Understand It takes time to understand. Even you ask me if I understand? Well, I don't know. 2019.5.20 Admire (Shows Godel's paper by projector) I don't understand this, no one understands this, but we can admire this. 2019.5.27 Arithmetic hierarchy (Draws the arithmetic hierarchy over half a whiteboard). For us computer scientists, computer scientists, what do we care about? (fills a fingernail size region on delta_0) We only care about this. 2019.5.27 Problem I have a problem, I don't know what to teach next week. 2019.6.3 Messed up Sorry, I am messed up. I am always messed up. 2019.6.3 hierarchy As usual, hierarchy means there is, hierarchy. Level. 2019.6.3 Different What is the difference between mathematicians and computer scientists? Mathematicians say this language is easy. What is it, it's \Sigma^0_3. A language is hard, it's \pi^1_4. For computer scientists, NP, oh! this problem is so hard. 2019.6.3 Take pictures You all take pictures. This makes me nervous, maybe the index is wrong. 2019.6.3 End of course I admit that I do not teach as well as the year before, but I hope you learned something... You can do anything you want now, you know some logic. The most important thing is, do not say some nonsense about incompleteness theorem. σ 评分方式(给分甜吗？是紮实分？) 100% 作业，习惯准时交作业的人应该不是问题。 不会写的人总有助教同学可以让你问到自认会写为止。 ρ 考题型式、作业方式 四次作业各五题。作业都像考卷般，每题配好约一页大的空白作答区， 因为老师看到乱乱的格式会心情不好~ 缴交方式相当神奇，可以上课交或是死线前塞进老师办公室门缝。 作业会归还，至少我没看过有谁的作业上出现脚印啦。 ω 其它(是否注重出席率？如果为外系选修，需先有什麽基础较好吗？老师个性？ 加签习惯？严禁迟到等…) 我不知道老师在不在意出席人数，反正不会影响成绩。 外系的话我不确定，但我可以肯定你不需要懂中/英文语意学，也能学到逻辑。 如果知道「资工系的证明」标准在哪，或是你是符号大师，应该会轻松不少。 加签好像是全签，期末班上是 44 个人吧。 Ψ 总结 其实我只是毕业前想用 112ip 赚 P 币顺便清硬碟而已。 --

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