The objective of SCG(P) is to distinguish correctly between good and bad claims in the context of a playground P. A playground is defined by a logical What about logical deduction in SCG? What are the axioms in SCG? Claims that are impossible to refute? Refutation protocol for axioms? formalize propagation of refutability instead of validity. Refutation systems are inference systems, just like traditional axiomatic systems, but they generate non-valid formulas rather than valid ones. They consist of refutation axioms (which are non-valid formulas) and refutation rules (which are rules preserving non-validity). http://staff.science.uva.nl/~johan/LO-GA-gabbay.pdf Open problems in Logic and Games In SCG(D), scholars collaborate and compete in two-player games and propose and oppose claims in domain D. The claims are predicting the outcome of refutation protocols exchanging instances and solutions between scholars. Scholars gain reputation by successfully defending their claims or by successfully refuting claims of others.
The game goal is to find the strongest claims and corresponding algorithms in domain D to defend them.
alternative: higher reputation = better health
Mathematical claims expressible in predicate logic can be easily expressed in SCG. But SCG allows claims with secrets which go beyond what is expressible in predicate logic.