Dialogical semantics
Example. Let p be true and q be false in M. Then the rules allow two games G(?p ? ?q; M):
2. In G(p; M) the roles of the players change.
3. The initial verifier must falsify p, and loses the game since p is true in M.
2. In G(q; M) the roles of the players change.
3. The initial verifier must falsify q, and wins the game since q is false in M.
1. The initial verifier chooses to play G(?p; M) or G(?q; M).