Approaches to Independence Friendly Modal Logic

The aim of the present paper is to discuss two different approaches for formulating independence friendly (IF) modal logic. In one of them, the language of basic modal logic is enriched with the slash notation familiar from IF first-order logics, and the resulting logic is interpreted in terms of games and uniform strategies. A different approach is formulated in the present paper: an IF modal logic is defined by imposing conditions on its structural relationships to other logics, namely a specified modal logic (say, basic modal logic), its first-order correspondence language, and IF logic. We compare logics emerging from the two approaches. More generally, the issue of the Eigenart of IF modal logics is addressed.