SUBSTRUCTURAL LOGICS
Logics individuated by their treatment of the structural rules of the sequent calculus—weakening, contraction, exchange, and associativity. Restricting or removing these rules makes the logic sensitive to the multiplicity, order, and use of premises, turning assumptions into consumable resources.
The division is organized by which structural rule is withheld. Linear entries drop weakening and contraction, tracking resource use exactly. Affine entries drop contraction only. Relevant entries drop weakening, enforcing premise relevance. Ordered entries drop exchange, making premise order significant. Nontransitive entries drop cut, which is the move the semantic-paradox literature made when it declined to give up any connective. Root entries cover implication-containment and connexive systems defined by related structural constraints.