Referential logic of proofs

We introduce an extension of the propositional logic of single-conclusion proofs by the second-order variables denoting the reference constructors of the type “the formula which is proved by x.’’ The resulting Logic of Proofs with References, FLP ref , is shown to be decidable, and to enjoy soundness and completeness with respect to the intended provability semantics. We show that FLP ref provides a complete test of admissibility of inference rules in a sound extension of arithmetic. This paper may be regarded as a contribution to the theory of automated reasoning systems.