Independence-friendly logic

Summary

Independence-friendly logic (IF logic; proposed by Jaakko Hintikka and Gabriel Sandu (philosopher) in 1989) is an extension of classical first-order logic (FOL) by means of slashed quantifiers of the form $(\exists v/V)$ and $(\forall v/V)$, where $V$ is a finite set of variables. The intended reading of $(\exists v/V)$ is "there is a $v$ which is functionally independent from the variables in $V$". IF logic allows one to express more general patterns of dependence between variables than those which are implicit in first-order logic. This greater level of generality leads to an actual increase in expressive power; the set of IF sentences can characterize the same classes of structures as existential second-order logic ($\Sigma^1_1$).