[Cs5500] CS5500 - Rule for Agreement

[Yue Liu]

Hi Professor Lieberherr,

The process of negating an SCG claim/protocol is switching the two roles in
protocol steps. If the original claim C which proposed by Alice requests
the claimee Bob to provide an instance first, claimer Alice will provide the
solution in the second step. So the negated claim !C will ask the claimer to
provide an instance first, then ask the claimee to provide a solution for
that instance. In other words, a negated claim means the protocol in that
claim is negated.

For example:
Alice made a claim AC: For all instances in the instance set exist a
solution such that a predicate holds.
If Bob refuted AC, he needed to provide a instance and Alice will provide a
solution.

Alice made the negated claim !AC: Exist an instance in the instance set for
all solutions such that a predicate holds.
If Bob refuted !AC, Alice should provide an instance and Bob will provide a
solution.

Best Regards,
Yue

On Mon, Apr 4, 2011 at 9:58 AM, Karl Lieberherr <lieber at ccs.neu.edu> wrote:

> 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
> >
> >
>
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