Dependence logic with a majority quantifier

TL;DR

This paper explores an extension of dependence logic with a majority quantifier, demonstrating its equivalence to second-order logic with majority quantifiers and its ability to characterize the counting hierarchy in complexity theory.

Contribution

It introduces a new logical framework D(M) with a majority quantifier and proves its expressive power matches that of second-order logic with all arities of majority quantifiers.

Findings

D(M) is expressively equivalent to second-order logic with majority quantifiers.

D(M) captures the counting hierarchy in descriptive complexity.

The results connect dependence logic extensions to complexity class characterizations.

Abstract

We study the extension of dependence logic D by a majority quantifier 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, D(M) captures the complexity class counting hierarchy.