Hierarchies in independence logic

TL;DR

This paper explores the expressive capabilities of various fragments of inclusion and independence logic under different semantics, establishing their relationships with existential second-order logic and revealing their equivalences.

Contribution

It characterizes the expressive power of restricted fragments of inclusion and independence logic and compares their semantics, connecting them to well-known logical systems.

Findings

Fragments with limited universal quantifiers relate to existential second-order logic.

Under strict semantics, inclusion logic equals existential second-order logic.

The study clarifies the impact of semantics on the expressive power of these logics.

Abstract

We study the expressive power of fragments of inclusion and independence logic defined either by restricting the number of universal quantifiers or the arity of inclusion and independence atoms in formulas. Assuming the so-called lax semantics for these logics, we relate these fragments of inclusion and independence logic to familiar sublogics of existential second-order logic. We also show that, with respect to the stronger strict semantics, inclusion logic is equivalent to existential second-order logic.