Complexity of Two-Variable Dependence Logic and IF-Logic

We study the two-variable fragments D
²
and IF
²
of dependence logic and independence-friendly logic. We consider the satisfiability and finite satisfiability problems of these logics and show that for D
²
, both problems are NEXPTIME-complete, whereas for IF
²
, the problems are undecidable. We also show that D
²
is strictly less expressive than IF
²
and that already in D
²
, equicardinality of two unary predicates and infinity can be expressed (the latter in the presence of a constant symbol).An extended version of this publication can be found at arxiv.org.