Complexity of Two-Variable Dependence Logic and IF-Logic

We study the two-variable fragments D² and IF² of dependence logic and independence-friendly logic. We consider the satisfiability and finite satisfiability problems of these logics and show that for D², both problems are NEXPTIME-complete, whereas for IF², the problems are undecidable. We also show that D² is strictly less expressive than IF² and that already in D², 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.