 According to Schroeder-Heister 2009, Gentzen’s sequent calculus is a “more adequate formal model of hypothetical reasoning” than natural deduction, and proof-theoretic semantics has also been developed with respect to various kinds of sequent calculi. Sequent systems for connexive logics can be found in Wansing 2007, Wansing 2008, McCall 2014, Kamide and Wansing 2011, 2016, Kamide, Shramko and Wansing 2017, and Kamide 2019.