 Differently from dependence and independence logic, inclusion logic is (sentence-wise) strictly weaker than existential second order logic. In fact, it can be shown (Galliani &amp; Hella 2013) to be equivalent to the positive fragment of greatest fixed point logic, and, therefore, to capture PTIME properties of models over finite ordered models. Formula-wise, inclusion logic is strictly weaker than independence logic but incomparable with dependence logic: indeed, the satisfiability conditions of its formulas are not downwards closed, but they are closed by unions in the sense that 