Dependence Logic with a Majority Quantifier

Arnaud Durand, Johannes Ebbing, Juha Kontinen, Heribert Vollmer

Abstract: We study the extension of dependence logic \(\mathcal {D}\) by a majority quantifier \(\mathsf{M}\) over finite structures. We show that the resulting logic is equi-expressive with the extension of second-order logic by second-order majority quantifiers of all arities. Our results imply that, from the point of view of descriptive complexity theory, \(\mathcal {D}(\mathsf{M})\) captures the complexity class counting hierarchy. We also obtain characterizations of the individual levels of the counting hierarchy by fragments of \(\mathcal {D}(\mathsf{M})\).