 Another interesting classification of negation operators arises if it is assumed that the language under consideration contains a primitive implication connective, \(\rightarrow\), that is not defined by putting \((A \rightarrow B) \coloneq (\osim A \vee B)\), or a primitive so-called co-implication (or subtraction) operation, \(\coimp\), not defined by putting \((A \coimp B) \coloneq (A \wedge \osim B)\), or both. The standard understanding of negated implications is conveyed by the equivalence \(\osim (A \rightarrow B) \leftrightarrow (A \wedge \osim B)\). Dually, the classical reading of negated co-implications is expressed by \(\osim (A \coimp B) \leftrightarrow (\osim A \vee B)\). Co-implication is the dual of implication, insofar as it stands to disjunction as implication stands to conjunction: