Semantic minimalism for logical constants

In [31], I defended a minimalist account of meaning for logical constants as a way to ward off Quine's meaning variance charge against deviant logics. Its key idea was that some deviant propositional logics share with classical logic the operational meanings of all their connectives, as encoded in their sequent calculus operational rules, yet validate different sequents than classical logic - therefore, we can have genuine rivalry between logics without meaning variance. In his [19], Ole Hjortland levelled several objections at this view. The aim of this paper is to address these criticisms, highlighting at the same time the role played by logical consequence in this version of semantic minimalism.