\section{Problem Solving Courses}

http://www.ccs.neu.edu/home/lieber/evergreen/specker/SCG-Teach/teach.html

\section{RULES FOR REPUTATION COMPUTATION}

We have developed a computational model for scientific communities
to foster better innovation and better education.
Central to a scientific community is refutation and how
it affects reputation of the scholars. The following rules
define the reputation mechaism of SCG.

There is some redundancy in those rules but I believe no contradiction.

Scholars propose and oppose claims and agree on claims.
Oppose means (refute | strengthen). 
Refute is determined by a refutation protocol.
Strengthening is reduced to refutation.
Agreement is also reduced to refutation.

Strengthening:
When claim C is strengthened by Bob to C', Alice must try to refute C' and the strengthening holds
only if Bob defends C'.
strengthenP(C,C') must hold.
When scholar Bob successfully strengthens a claim of Alice, Bob wins reputation:
Bob  + ClaimConfidence + |quality(C)-quality(C')|
When scholar Alice successfully defends her own claim against Bob, Alice wins reputation.
Alice + ClaimConfidence

There is a gray zone with strengthening. Let's assume we have
quality(C) < q < quality(C') and q is the quality achieved by the solution.
Then both Alice and Bob have lost because Bob did not achieve what he
claimed and Alice claim was shown not to be optimal.
We make the simplifying assumption that Bob only wins
if he defends C'.

Agreement:
When Bob agrees on claim C with Alice, 
(1) Bob must defend C against Alice (if not, Bob loses)
(2) Bob must refute C' = C minimally strengthened along
  quality dimension (using the configuration file constant minStrengthen) 
  with Alice as defender (if not, Bob loses).
Then Alice must do the same:
(1) Alice must defend C against Bob (if not, Alice loses)
(2) Alice must refute C' with Bob as defender (if not, Alice loses)
If all those protocols produce the result as described,
the claim goes into the social welfare set (the knwledge base
of claims believed to hold and having maximum strength).

All scholars start with reputation 100.
Reputation is zero sum.
Alice proposes, Bob opposes.

When scholar Bob successfully refutes a claim of Alice, Bob wins reputation:
Bob  + ClaimConfidence

When scholar Alice successfully defends her own claim against Bob, Alice wins reputation.
Alice + ClaimConfidence

summary:
Bob: + ClaimConfidence * result
Alice: - ClaimConfidence * result

When scholar Bob successfully strengthens a claim C of scholar Alice to claim C', 
Bob wins reputation:
Bob  + ClaimConfidence + |quality(C)-quality(C')|

Checking of instances and solutions:

0. An InstanceSet must be valid.
1. All instances are in Instance.
2. A solution s in Solution for instance i in Instance must satisfy: valid(i,s).
3. When an instance i in Instance is provided, InstanceSet.belongsTo(i) holds.

In one domain, multiple InstanceSet are allowed.
In one play ground, multiple claims are allowed.

Some rules are enforced syntactically by the structure of a game definition.
Only one domain definition.
Multiple different claim languages are allowed, e.g., claims and negated claims.

Avatars with a negative reputation are kicked from the game.

The constants in the configuration file are enforced.

Axioms

Scholars gain reputation either by opposing (refuting or strengthenin) other scholars' claims
or by having their claims defended against other agents.
Scholar's gain from their claim is proportional to both
the confidence of their claim and the result of the refutation protocol
(a value in [-1,1]).

One scholar's reputation gain is another
scholar's reputation loss. The sum of all agent's reputation is preserved.

Arguments (instances and solutions obtained from the refutation
protocol) recognize claims by
a recognition factor in [-1,1].
A recognition factor of 1 means that the other scholar Bob has
completely failed to discount Alice' claim.
We say that Alice has defended the claim.
A recognition factor of -1 means that the other
scholar has completely succeeded to refute the claim.
We say that Bob has successfully refuted the claim.

Claims have a confidence in [0,1].

The scholar's confidence reflects the amount of effort
made by the scholar to refute the claim.
If it is a mathematical claim, it is the amount of effort
spent to try to prove the claim
(i.e. turning it into a theorem).
Scholar's reputation is the accumulation of the scholar's initial reputation
and its reputation gains and losses; thus reflecting the past performance of the scholar.

Those axioms define a family of mechanisms that can be used
to implement the game.

