Dialogue games in logic
Dialogical semantics: establish truth (i.e, in a single interpretation)
Myself tries to show the truth of a sentence, and Nature its falsity
Dialogical proof theory: establish logical truth (i.e., in any interpretation)
Myself wants to construct a model for a sentence S and Nature tries to show that there is no such model
? Cf. Hintikka and Sandu (1997). Game-theoretical semantics. Handbook of logic and language
? Hintikka and Sandu speak of games of verification and falsification vs. games of formal proof