 This duplication of the connectives actually leads to a much clearer understanding of the conflict between classical and intuitionistic logic. For example, the law of excluded middle (\(A\) or not-\(A\)) is considered valid in the classical world and absurd in the intuitionistic one. But in linear logic, this law has two readings: the additive version \((A \oplus \neg A)\) is not provable and corresponds to the intuitionistic reading of disjunction; the multiplicative version \((A \lpar \neg A)\) is trivially provable and simply corresponds to the tautology \((A\) implies \(A)\) that is perfectly acceptable in intuitionistic logic too.