Inequalities in De Morgan systems. I

In a Boolean algebra, every element has two canonical forms, its disjunctive normal form (BDNF) and its conjunctive normal form (BCNF). If these elements are viewed in the algebra consisting of the unit interval with operations min, max, and the usual negation, the inequality BDNF⩽BCNF always holds. If the operations min and max in this algebra are replaced by a t-norm and its t-conorm dual to the usual negation, the resulting inequality holds sometimes and fails sometimes. The paper examines this phenomenon, especially in the two variable case