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We study the expressive power of fragments of inclusion and independencelogic defined by restricting the number k of universal quantifiers in formulas.Assuming the so-called strict semantics for these logics, we relate thesefragments of inclusion and independence logic to sublogics ESO_f(k\forall) ofexistential second-order logic, which in turn are known to capture thecomplexity classes NTIME_{RAM}(n^k).

Hierarchies in independence and inclusion logic with strict semantics