A Resolution Calculus for Recursive Clause Sets

Proof schemata provide an alternative formalism for proofs containing an inductive argument, which allow an extension of Herbrand’s theorem and thus, the construction of Herbrand sequents and expansion trees. Existing proof transformation methods for proof schemata rely on constructing a recursive resolution refutation, a task which is highly non-trivial. An automated method for constructing such refutations exists, but only works for a very weak fragment of arithmetic and is hard to use interactively. In this paper we introduce a simplified schematic resolution calculus, based on definitional clause forms allowing interactive construction of refutations beyond existing automated methods. We provide an example based on an important theoretical case and a procedure for constructing an inessential cut normal form schema.