Abstract The fluted fragment lacks the Craig Interpolation Property. In this paper we establish a weakened form of interpolation. Given an entailment in the fluted fragment, we distinguish predicates that only take an argument sequence starting with $$x_1$$ x 1 from those that do not. A predicate of the former kind is allowed to appear in a weak interpolant only if it occurs in both the premise and the conclusion; and any predicate of the latter kind can be used in a weak interpolant no matter whether it is in the shared signature. Our proof also shows that the weakened interpolation holds in every finite variable subfragment of the fluted fragment. In addition, this work provides a generalization of A. Herzig’s translation of the ordered fragment, as well as a new proof of the finite model property of the fluted fragment.

Abstract We investigate the uniform fluted fragment, a subfragment of the fluted fragment obtained by imposing the uniformity restriction on Boolean combinations. First, with a novel trick in model construction, we prove that the uniform fluted fragment has an exponentially bounded model property. It follows that, unlike the full fluted fragment (where satisfiability is non-elementary), satisfiability in this subfragment is NExpTime -complete. Second, we formulate a bisimulation for the subfragment, and establish a characterization of its expressive power in the style of van Benthem. Finally, we show that the uniform fluted fragment is equi-expressive with the uniform forward fragment (if we consider only sentences), and that satisfiability in the latter is also NExpTime -complete.