CS67664 Reasoning about Knowledge

CS 6764: Reasoning About Knowledge - Spring 2015

Instructor: Joe Halpern, 414 Gates, halpern@cs.cornell.edu, 5-9562
Admin:Randy Hess, 323 Gates, rbhess@cs.cornell.edu, 5-0985;
TAs:, Nan Rong and Samantha Leung
Office hours: Halpern: Wednesdays, 1:30 - 2:30, 414 Gates; Rong and Leung: Tuesdays, 3-4, G17 Gates

Text: Reasoning About Knowledge (Fagin, Halpern, Moses, Vardi). (It should be available in the bookstore. The paperback version is best, but the hardcover version is OK too. The paperback version corrects a number of typos and minor errors in the hardcover version.)
Grading: There will be no tests or final examination. There will be problems handed out, typically 3 every Thursday, from the book. The grade will be based completely on your performance on the problems. Problems are always due two weeks after they're handed out. If you hand them in one week after they're handed out, I will grade them and return them the following week. You can then redo any problem that you seriously attempted and hand it in again, to improve your grade. On a redo, you can get a maximum of 1 point less than the original value of the problem. (That is, if the problem was originally out of 10, the most you can get is 9.) I will take the higher grade.
Academic Integrity: It's OK to discuss the problems with others, but you MUST write up solutions on your own, and understand what you are writing.
Course Outline: We will be following the text very closely. Very roughly, we will be covering one chapter per week. Topics include modal logic, common knowledge, applying reasoning about knowledge in distributed systems (and economics, depending on interest), knowledge-based programming, dealing with logical omniscience, algorithmic knowledge.
Course Outline: We will be following the text very closely. Very roughly, we will be covering one chapter per week. Topics include modal logic, common knowledge, applying reasoning about knowledge in distributed systems (and economics, depending on interest), knowledge-based programming, dealing with logical omniscience, algorithmic knowledge.

Homework

Note: you can find your grades and solutions to the homework at CMS.

Week 1: handed out 1/29; due 2/12 (hand it in 2/5 for a second chance)

Read Chapters 1 and 2.
Do 1.2, 2.4, 2.11. (If you have the hardcover version of the text, ignore the comment in part 2.4(d) about edges disappearing; this comment does not appear in the paperback version -- for good reason.)

Week 2: handed out 2/5; due 2/19; hand it in 2/12 for a second chance)

Read Chapters 3.1 and 3.2
Do 2.9, 2.12, 3.10, and 3.14. For 2.12 I want a semantic proof. Don't use the axioms. Rather, you should do proofs in the style of the other proofs in Chapter 2, where you talk about what formulas are true at various states. You can assume that the \K_i relations are equivlaence relations, because that's what's assumed in Chapter 2. On the other hand, for 3.10(b), (c) and 3.14, I want a syntactic proof. That is, you should show explicitly how the relevant formulas are derivable from the axioms (without appealing to any of the soundness and completeness theorems).

Week 3: handed out 2/12; due 2/26 (hand it in 2/19 for a second chance)

Read Chapter 3
Do 3.13(c),(d),(e),3.16, 3.17, 3.20. (I did 3.13(c) iin class, but it's a good exercise to write out.)
If you handed in homework 1 last week, please email Nan (rongnan@cs.cornell.edu) your grade. (We're going on the honor system, but Nan does remember most of the grades ...)

Week 4: handed out 2/19; due 3/5 (hand it in 2/26 for a second chance)

Read Chapter 4
Do 4.9, 4.18, 4.20

Week 5: handed out 2/26; due 3/11 (hand it in 3/4 for a second chance)

Read Chapter 4
Do 4.24, 4.25, 4.28. (Warning: some of these problems require thought. Don't leave it to the last minute!). Note that there is a typo in 4.24. On line 4 of p.156, it should say r(m'-k), not r(m-k). A complete list of known typos can be found at http://mitpress.mit.edu/books/reasoning-about-knowledge. (Click on the "errata" link on the left-hand side of the page.) I would be happy to hear about other typos that you find.

Week 6: handed out 3/5; due 3/19 (hand it in 3/12 for a second chance)

Read Chapters 5 and 6.1
Do 5.11, 6.2
You can now hand in homework on CMS.

Week 7: handed out 3/12; due 3/26 (hand it in 3/19 for a second chance)

Read Chapter 6
Do 6.6, 6.8, 6.13
You can now hand in homework on CMS.

Week 8: handed out 3/19; due 4/9 (hand it in 3/26 for a second chance)

Do 6.14, 6.16, 6.19, 6:23
The Ariel Rubinstein paper that I talked about in the last class can be found here. The paper is short and fun to read. I strongly encourage you to take a look.

Week 9: handed out 3/26; due 4/16 -- three weeks from now, because of spring break (had it in 4/10 for a second chance).

Read Chapter 7
Do 7.3, 7.4, 7.7
The paper that adds counterfactuals to knowledge-based programs can be found here; the slides for a talk on the paper are here.

Week 10: handed out 4/9; due 4/23 (had it in 4/16 for a second chance).

Read Chapter 8, 9.1-9.3
Do 8.5, 8.9, 9.8, 9.14

Week 11: handed out 4/16; due 4/30 (had it in 4/23 for a second chance).

Read Chapter 9
Do 9.22, 9.42, 9.45
The puzzle briefly discussed in class on Tuesday can be found here. If elementary school students can do it, you should be able to too (especially since they don't have the benefit of knowing about Kripke structures, which really help!)
- Update #1: Apparently, this was not intended for elementary school students, but was a problem on the Math Olympiad. (Details can be found here; thanks to Jun Le for pointing this out.) You should still be able to do it easily though!
- Update #2: Here is a version that's not so easy (see me if you'd like some hints):

Week 12: handed out 4/23; due 4/7 (either email it to Nan or Sam, post it on CMS or hand or hand it in in class on 4/5; hand it in 4/30 for a second chance). This is the last homework!

Read Chapters 10 and 11
Do Do 9.49 [5 points], 10.3 [5 points], 11.2; also show that every a.m.p and every a.r.m.p has temporal imprecision.
The slides that I used in the last two classes can be found here. The material on which the talk is based can be found here and here.

Parting comments:

You can find some discussion of characterizing solution concepts in terms of common knowledge of rationality here.
As Michael Usher pointed out, for the question asking you to show that amps and armps display temporal imprecision, you have to assume that messages take at least one round to arrive. Sorry about that!
I should be able to post grades sometime towards the end of next week. I'll send out an email when they're available.
Thanks again for being a great class!