Discussion Questions for "Knowledge and Common Knowledge in a Distributed Environment"

versey-sherry commented 3 years ago

@ksuhr1 @git-ram @maxwellrbradley @andavid0

maxwellrbradley commented 3 years ago

@lkuper Lindsey, the question responses are now ready for you to review.

lkuper commented 3 years ago

Can you leave the "Discussion summary for Q1", "Discussion summary for Q2", etc. headings on the page so we can tell where the question ends and the discussion begins?

Other than that, the main issue is that there is some confusion between "everyone knows that everyone knows P" ("E^2 knowledge" in terms of the paper) and "common knowledge". Common knowledge of P is when everyone knows that everyone knows P, but also everyone knows that everyone knows that everyone knows P, and so on, infinitely. It's true that E^2 knowledge is useful, but it's not the same as common knowledge. (Also, E^2 knowledge is achievable in a distributed system under the omission model, but common knowledge is not. Same for E^k for any finite k.)

Q1:

"The role of the father letting everyone that everyone knows" -- there's a word missing here
"common knowledge, where everyone in the system knows that everyone else in the system knows the relevant information." -- yes, the father's announcement does actually establish common knowledge (as discussed in the paper), but here it sounds like you think common knowledge is E^2 knowledge.
I think the party example is good, but "the host disseminating information about the overall set of people confirms that the party is happening" is not how I would phrase it. It's not that it confirms that the party is happening (they all already knew that), it's that now they know that everyone else knows, too.

Q2: all looks good except the last part, which has some confusion between E^2 knowledge and common knowledge.

Q3: I'm not sure what you mean by "a dual form of" at the end. Halpern and Moses meant "dual" in the mathematical sense. It's a slippery concept to pin down, but it involves something like two different points of view of looking at the same object, where those two different points of view mirror one another. In class we talked about "exists" and "for all" being dual. More examples here: https://en.wikipedia.org/wiki/Duality_(mathematics)#Duality_in_logic_and_set_theory

git-ram commented 3 years ago

@lkuper We updated the answers according to the points you mentioned. Please let us know if anything is still unclear. Thanks

lkuper / CSE232-2020-10

Discussion Questions for "Knowledge and Common Knowledge in a Distributed Environment" #14