On the complexity of disjunction and explicit definability properties in some intermediate logics

In this paper we provide a uniform framework, based on extraction calculi, where to study the complexity of the problem to decide the disjunction and the explicit definability properties for Intuitionistic Logic and some Superintuitionistic Logics. Unlike the previous approaches, our framework is independent of structural properties of the proof systems and it can be applied to Natural Deduction systems, Hilbert style systems and Gentzen sequent systems