Dialogical semantics
It turns out that there is a natural game-theoretical semantics that is equivalent to standard first-order logic
? If the logical language allows branching quantifiers, a natural game-theoretical semantics exists, while Tarskian semantics does not help.
? In game-theoretical semantics, truth and falsity are still each other’s complement, but there can be sentences that are neither true nor false.
? Cf. Hintikka and Sandu