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.