Status of negation as a structural operator

Determine whether negation should be understood not merely as a logical constant alongside conjunction, disjunction, and implication, but as a structural operator responsible for regulating polarity and thereby contributing to the dual character of classical logic.

Background

The paper develops a bilateral framework in which acceptance and rejection are represented as positive and negative polar positions, while negation mediates the relation between them. In this framework, acceptance of A is related to rejection of ¬A, and rejection of A is related to acceptance of ¬A.

The authors suggest that this mediating role may justify treating negation as more than an ordinary logical constant. However, the paper does not settle whether negation has structural status in classical logic; it identifies this as a separate investigation connected with the regulation of polarity and the dual character of classical logic.