RELEVANT LOGIC
Logics that drop weakening in order to enforce relevance: the antecedent of a valid implication must actually be used in deriving the consequent, blocking the paradoxes of material and strict implication. The characteristic semantics is the Routley-Meyer ternary relation, with the variable-sharing property as a hallmark.
Entries range over the relevant family and neighboring substructural systems. Relevance logic and relevant implication give the core; Ackermann's systems, ticket entailment, and mingle mark historic and axiomatic variants; BCK and contraction-free logics sit at the boundary where further structural rules are tuned. The substructural-logics entry serves as a hub relating these disciplines.