 For this section the focus will be on rules governing the various connectives, beginning with a deferred topic from Section  2:  the transfer of Carnap-inspired questions of the range of valuations on which the sequents provable in this or that logic hold to question about the range of valuations on which the sequent-to-sequent rules preserve the property of holding. We will also revisit the sequent-calculus operational rules from early in Section  2  and look at some of their properties, as well as at some interesting variations on the structural rules which work alongside them. One topic—or pair of topics—raised by such investigations is the issue of the existence and uniqueness of connectives exhibiting prescribed logical behaviour (such as might be enshrined in various rules), an issue bearing on all approaches to logic and not just the sequent calculus approach. Finally we look at a pair of concepts applying to connectives as they behave in particular logics: the concept of a universally representative connective and the concept of a ‘special’ connective.