Hierarchies in inclusion logic with lax semantics

TL;DR

This paper investigates the expressive power of inclusion logic fragments under lax semantics, revealing a collapse in the universal quantifier hierarchy and a strict arity hierarchy linked to fixed point logics.

Contribution

It establishes the collapse of the universal quantifier hierarchy and proves the strictness of the arity hierarchy in inclusion logic under lax semantics.

Findings

Universal quantifier hierarchy collapses at the first level.

Arity hierarchy is strict, related to fixed point logics.

Provides insights into the expressive limits of inclusion logic fragments.

Abstract

We study the expressive power of fragments of inclusion logic under the so-called lax team semantics. The fragments are defined either by restricting the number of universal quantifiers or the arity of inclusion atoms in formulae. In case of universal quantifiers, the corresponding hierarchy collapses at the first level. Arity hierarchy is shown to be strict by relating the question to the study of arity hierarchies in fixed point logics.