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. When claim C is strengthened by Bob to C', Alice must try to refute C' and the strengthening holds only if Bob defends C'. strengthen(C,C') must hold. When Bob agrees on claim C with Alice, (1) Bob must defend C against Alice (2) Bob must refute C' = C minimally strengthened along quality dimension (using the configuration file constant minStrengthen) with Alice as defender. Then Alice must do the same: (1) Alice must defend C against Bob (2) Alice must refute C' with Bob as defender If all those protocols produce the result as described, the claim goes into the social welfare set. 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 proportional to the quality difference. Bob + |quality(claim) - quality(solution)|*AliceClaimConfidence When scholar Alice successfully defends her own claim against Bob, Alice wins reputation. Alice + When a scholar successfully strengthens a claim of another scholar, she wins reputation proportional to the quality difference. When a scholar Bob agrees on claim C, but cannot defend C against the other player Alice, Bob loses reputation. Formulas: ? Checking of instances and solutions: In one game, multiple InstanceSet and Claimdefinitions are allowed. 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. 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.