 In CS4 the modal operators □ and ◊ are syntactic duals of each other: the equivalence between □A and ~◊~A and between ◊A and ~□~A is provable. Kamide and Wansing (2011) also present a cut-free sequent calculus for a connexive constructive version CS4d– of S4 without syntactic duality between □ and ◊. The relational possible worlds semantics for CS4d– is not fully compositional, cf. Odintsov and Wansing 2004. CS4d– is faithfully embeddable into positive S4 and decidable. Moreover C is faithfully embeddable into CS4d–.