A Parametric Interpolation Framework for First-Order Theories

Craig interpolation is successfully used in both hardware and software model checking. An important class of state-of-the-art interpolation algorithms is based on recursive procedures that generate interpolants from refutations of unsatisfiable conjunctions of formulas. We analyze this type of algorithms and develop a theoretical framework, called a parametric interpolation framework, for arbitrary first-order theories and inference systems. Our framework is able to compute interpolants of different structure and strength, with or without quantifiers, from the same proof. We show that two classes of well-known interpolation algorithms, that address local proofs in first-order logic and the propositional hyper-resolution system, are instantiations of our framework.