Independence and games

Abstract

Hintikka and Sandu have developed IF logic as a genuine alternative to classical first-order logic : liberalizing dependence schemas between quantifiers, IF would carry out all the ideas already underlying classical logic. But they are alternatives to Hintikka’s game-theoretic approach; one could use instead Henkin quantifiers. We will present here some arguments of both technical and philosophical nature in favor of IF. We will show that its notion of independence, once extended to connectives, can indeed claim to be fully general, and that IF logic provides an analysis of independence patterns. This last point will be argued for thanks to an explanation of the epistemic content of IF, through a partial translation into modal logic.