  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.
