 Of course, one expects the addition of new rules to make for the provability of new sequents, but the extension should be conservative in the sense that no new sequents exclusively involving the old vocabulary become provable. Belnap’s discussion suggests that the existence of a connective obeying certain rules should be conceded by someone endorsing a particular proof system if and only if the addition of that connective to the language and those rules to the proof system yields a conservative extension. (There are other things one might mean by the question of whether from the perspective of a given logic, a connective with such-and-such logical powers exists—most evidently, whether or not such a connective is already definable in the logic. Showing that rules ascribing the powers in question would extend the logic non-conservatively would be one dramatic way of showing no such connective to be definable, but since it could fail to be definable while still being conservatively addable, the questions need to be kept distinct.)