It has been argued that a combination of game-theoretic semantics and independence-friendly (IF) languages can provide a novel approach to the conceptual foundations of mathematics and the sciences. I introduce and motivate an IF first-order modal language endowed with a game-theoretic semantics of perfect information. The resulting interpretive independence-friendly logic (IIF) allows to formulate some basic model-theoretic notions that are inexpressible in the ordinary quantified modal logic. Moreover, I argue that some key concepts of Kripke’s new theory of reference are adequately modeled within IIF. Finally, I compare the logic IIF to David Lewis counterpart theory, drawing some morals concerning the interrelation between metaphysical and semantic issues in possible-world semantics.
How to Lewis a Kripke-Hintikka / Torza, A. - In: SYNTHESE. - ISSN 0039-7857. - 190:4(2013), pp. 743-779. [10.1007/s11229-012-0201-0]