Combination of Uniform Interpolants via Beth Definability

Abstract Uniform interpolants were largely studied in non-classical propositional logics since the nineties, and their connection to model completeness was pointed out literature. A successive parallel research line inside automated reasoning community investigated uniform quantifier-free (sometimes referred as “covers”) first-order theories. In this paper, we investigate cover transfer theory combinations disjoint signatures case. We prove that, for convex theories, algorithms can be transferred under same hypothesis needed interpolation (i.e., equality interpolating property, aka strong amalgamation property). The key feature of our algorithm relies on extensive usage Beth definability property primitive fragments convert implicitly defined variables into explicitly defining terms. non-convex case, show by a counterexample that covers may not exist combined even case do exist. However, exhibit operating also special kinds combinations; these (called ‘tame combinations’) concern multi-sorted theories arising many model-checking applications (in particular, ones oriented verification data-aware processes).