Describes any deductive system that is characterized by a sequent calculus in which one or more of the structural rules—exchange, weakening, contraction—are not admissible. The restrictions in substructural logics frequently follow from a more nuanced reading of a sequent than is needed in classical logic. For example, in linear logic, cedents correspond to the resources used by a system and its sequent calculus is thus sensitive to the precise number of appearances of a formula in a cedent. Hence, the sequents $\phi ,\phi \Rightarrow \psi$ and $\phi \Rightarrow \psi$ must remain distinct, demanding that contraction and weakening be applied only in very limited circumstances.

Substructural logics also share a great deal in common with relevant logics. For example, in the classical sequent calculus, the structural rule of weakening is used to employ many theorems for which the variable sharing property fails, e.g, the derivation of $q\to \left(p\to p\right)$:

makes essential use of the rule of weakening.