On the formal semantics of IF-like logics

In classical logics, the meaning of a formula is invariant with respect to the renaming of bound variables. This property, normally taken for granted, has been shown not to hold in the case of Information Friendly (IF) logics. In this work we propose an alternative formalization under which invariance with respect the renaming of bound variables is restored. We show that, when one restricts to formulas where each variable is bound only once, our semantics coincide with those previously used in the literature. We also prove basic metatheoretical results of the resulting logic, such as compositionality and truth preserving operations on valuations. We work on Hodges' slash logic (from which results can be easily transferred to other IF-like logics) and we also consider his flattening operator, for which we give a game-theoretical semantics.