Semantic games with chance moves revisited: from IF logic to partial logic

We associate the semantic game with chance moves conceived by Blinov with Blamey’s partial logic. We give some equivalent alternatives to the semantic game, some of which are with a third player, borrowing the idea of introducing the pseudo-player called Nature in game theory. We observe that IF propositional logic proposed by Sandu and Pietarinen can be equivalently translated to partial logic, which implies that imperfect information may not be necessary for IF propositional logic. We also indicate that some independent quantifiers can be regarded as dependent quantifiers of indeterminate sequence, using the interjunction connective in partial logic. We conclude our paper by indicating some further research in a more general setting.