The meaning of the logical rules is to be found in the rules themselves.
— J. Y. Girard in “On the Meaning of Logical Rules I: syntax vs. semantics”
There are two types of dualities in linear logic. Linear negation (⊥) carries the conjunctions to the disjunctions and back again, as equivalences (≡), like De Morgan’s laws in classical logic.
Additionally, the exponentials ? and ! link the additives and the multiplicatives, as linear biconditionals (o—o).