Linear Logic: the dualities

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).




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