  Carnap begins with a fixed formal language whose details need not concern us now. A class of atomic sentences in this language, containing exactly one of \(A\) or \(\neg A\) for each atomic sentence, is a state-description. In each state-description the truth or falsity of every sentence of the language is determined following the usual truth-functional rules—quantifiers are treated substitutionally, and the language is assumed to have ‘enough’ constants. Thus truth is relative to a state-description. Now Carnap introduces a stronger notion than truth, L-truth, intended to be “an explicatum for what philosophers call logical or necessary or analytic truth.” Initially he presents this somewhat informally, “a sentence is \(L\)-true in a state description \(S\) if it is true in \(S\) in such a way that its truth can be established on the basis of the semantical rules of the system \(S\) alone, without any reference to (extra-linguistic) facts.” But this is quickly replaced by a more precise semantic version, “A sentence is \(L\)-true if it holds in every state-description.”