[Cs5500] CS5500 - Rule for Agreement

[Karl Lieberherr]

Hi Yue:

I strengthen your definition by making it more general. You use a
protocol based on a mathematical claim.
The same agreement rule holds for any claim, also claims involving secrets.

In this case we also need the negation of a claim/protocol. Please can
you explain again
the process of negating an SCG claim/protocol.

-- Karl

On Mon, Apr 4, 2011 at 1:08 AM, Yue Liu <liuyue.ly at gmail.com> wrote:
> Hi Anush, Dan and Rashmi,
>
> I made the following claim about the rule for agreement. Please
> refute/strengthen it. Looking forward to your feedback.
>
>
> Rule for agreement:
>
> Alice proposes claim AC: For all F in IS exists J: fsat(F, J) >= tAC.
>
> The negated claim !AC will be: Exist F in IS for all J: fsat(F, J) < tAC.
>
> When Bob agrees on claim AC, the following conditions should be true.
>
> ·       Bob defends claim AC (meaning Bob proposes claim AC and Alice
> refutes AC)
>
> Alice gives F in IS,
>
> Bob gives J,
>
> If fsat(F, J) < tAC, Bob loses.
>
> ·       Otherwise, Bob refutes negated claim !AC (meaning Alice proposes
> claim !AC and Bob refutes !AC)
>
> Alice gives F in IS,
>
> Bob gives J,
>
> If fsat(F, J) < tAC, Bob loses.
>
> ·       Otherwise, Alice defends claim AC.
>
> Bob gives F in IS,
>
> Alice gives J,
>
> If fsat(F, J) < tAC, Alice loses.
>
> ·       Otherwise, Alice refutes negated claim !AC.
>
> Bob gives F in IS,
>
> Alice gives J,
>
> If fsat(F, J) <  tAC, Alice loses.
>
>
>
> Case 1:
>
> |-------|-------|----------->|
>
> 0         tAC     topt             1      tAC < topt
>
> If Bob and Alice are perfect, both Bob and Alice will be able to defend
> claim AC and refute negated claim !AC. Then the claim AC will be put into
> social welfare.
>
> This claim AC may be strengthened or refuted in future tournaments when
> scholars have better understanding and solution.
>
> Case 2:
>
> |-------|-------|----------->|
>
> 0         topt     tAC             1      tAC > topt
>
> If Bob and Alice are perfect, both Bob and Alice will not be able to defend
> claim AC or refute negated claim !AC. Then scholars will know the claim AC
> exceeds the optimal.
>
> Reputation:
>
> 1.     As the SCG encourages scholars to refute or strengthen claims, Bob
> will lose reputation as soon as he agreed on claim AC
> (-aliceClaimConfidence).
>
> 2.     Then as Bob proposed the same claim AC with a his confidence, if Bob
> can’t defend claim AC, he will lose reputation again (-bobClaimConidence).
>
> 3.     After Bob successfully defends AC, he will refute claim !AC. If he
> cannot  refute it, Bob lose reputation (-alice!ClaimConfidence).
>
> 4.     After Bob successfully refutes AC, Alice will defend AC. If she lost,
> Alice will lose reputation (-aliceClaimConfidence).
>
> 5.     At last, if Alice successfully defend AC, she will refute !AC. If she
> cannot refute it, Alice lose reputation (-bob!ClaimConfidence).
>
>
>
> Best Regards,
>
> Yue
>
>