  Došen is able to give characterizations which include systems of modal logic. He explicitly considers his work as a contribution to the logicality debate and not to any conception of proof-theoretic semantics. Sambin et al., in their Basic Logic (Sambin, Battilotti, and Faggian, 2000), explicitly understand what Došen calls double-line rules as fundamental meaning giving rules. The double-line rules for conjunction and disjunction are read as implicit definitions of these constants, which by some procedure can be turned into the explicit sequent-style rules we are used to. So Sambin et al. use the same starting point as Došen, but interpret it not as a structural description of the behaviour of constants, but semantically as their implicit definition (see Schroeder-Heister, 2013).