SCI–Sequent Calculi, Cut Elimination and Interpolation Property

We discuss the methods for providing sequent calculi for Suszko’s basic non-Fregean Logic with sentential identity SCI. After examination of possible strategies and already proposed systems we focus on the new calculus and its modification. It does not satisfy full cut elimination but a slightly generalised form of the subformula property holds for it. It is also standard in the sense of satisfying several conditions on rules formulated by Gentzen and his followers. We examine also the problem of providing a constructive proof of the interpolation theorem in the setting of this sequent calculus.