 The issue of uniqueness, as opposed to existence, of connectives (in the logically loaded sense of the term, naturally) is best approached by considering when a collection of rules governing a connective uniquely characterize that connective in the sense that if accompanied by corresponding rules governing a ‘duplicate’ version of that connective (of the same arity) result in the synonymy of compounds formed from the appropriately many components and the original connective with compounds formed from the duplicate connective from the same components. In a congruential setting the reference to synonymy can be replaced by one of equivalence, in the sense of ⊣⊢-equivalence in the consequence relation or Set-Fmla framework, with suitable variations for other frameworks. Without the assumption of congruentiality one should perhaps distinguish unique characterization to within synonymy from unique characterization to within equivalence. And because the rules in question may not be pure, but involve other connectives, it may be necessary to speak of # being uniquely characterized (by the given rules) in terms of the other connectives involved, so that when the reduplicated system is considered, # is replaced by its duplicate, #′, say, while the other connectives remain as they are. We will not be considering these complications here. It is easy to see that the natural deduction rules for the various connectives given in Section  2  as well as the sequent calculus rules all uniquely characterize the connectives they govern. (Note that, since this includes the introduction and elimination rules for →, which are shared by any natural deduction system for intuitionistic logic, the rules may uniquely characterize a connective which is not fully determined—not amenable to a truth-functional interpretation. The same applies in respect of negation, though we did not cover this in our discussion of natural deduction.) This feature is sometimes regarded as necessary for the connectives concerned to be regarded as logical constants, although, as explained in Section  1,  we are not pursuing that issue here.