Interpolation, amalgamation and combination : the non-disjoint signatures case

In this paper, we study the conditions under which existence of interpolants (for quantifier-free formulae) is modular, in the sense that it can be transferred from two first-order theories T1, T2 to their combination T1 ∪ T2. We generalize to the non-disjoint signatures case the results from [3]. As a surprising application, we relate the Horn combinability criterion of this paper to superamalgamability conditions known from propositional logic and we use this fact to derive old and new results concerning fusions transfer of interpolation properties in modal logic.