  Standard proof-theoretic semantics is assertion-centred in that assertibility conditions determine the meaning of logical constants. Corresponding to the intuitionistic way of proceeding, the negation ¬A of a formula A is normally understood as implying absurdity A →⊥, where ⊥ is a constant which cannot be asserted, i.e., for which no assertibility condition is defined. This is an ‘indirect’ way of understanding negation. In the literature there has been the discussion of what, following von Kutschera (1969), might be called ‘direct’ negation. By that one understands a one-place primitive operator of negation, which cannot be, or at least is not, reduced to implying absurdity. It is not classical negation either. It rather obeys rules which dualize the usual rules for the logical constants. Sometimes it is called the “denial” of a sentence, sometimes also “strong negation” (see Odintsov, 2008). Typical rules for the denial ~A of A are