Complexity of two-variable Dependence Logic and IF-Logic

TL;DR

This paper analyzes the computational complexity and expressive power of two-variable fragments of dependence and independence-friendly logic, revealing NEXPTIME-completeness for D^2 and undecidability for IF^2.

Contribution

It establishes the complexity classifications and expressive differences between D^2 and IF^2, including their satisfiability problems and expressive capabilities.

Findings

D^2 satisfiability is NEXPTIME-complete

IF^2 satisfiability is undecidable

D^2 can express equicardinality and infinity with constants

Abstract

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). This is an extended version of a publication in the proceedings of the 26th Annual IEEE Symposium on Logic in Computer Science (LICS 2011).