INCLUSION CRITERIA
An entry belongs in this subdivision if and only if it is individuated by the restriction or removal of cut—the transitivity of consequence—or by a related failure at the metainferential level.
Required: At least one of the following:
- A consequence relation that is not transitive, with the failure of cut as the system's distinguishing property
- A definition of validity by distinct standards for premises and conclusions (strict/tolerant and its relatives), from which the failure of cut follows
- A metainferential hierarchy in which the object-level logic is classical and the failure appears one level up
Not sufficient: A cut-elimination theorem, which shows cut is admissible and is a result about proofs (Metatheory/Proof-Systems). A logic that drops contraction to block Curry while keeping cut—that is noncontractive and belongs in Linear or Affine by which rule it drops, and is cross-listed here where the paradox motivation is the subject. A paraconsistent or paracomplete matrix (Algebraic/Many-Valued): the point here is that the matrix is not what changed.
Boundary: ST shares LP's and K3's matrices and differs from both only in how validity is defined across them—so it is placed by the metainferential failure, not by the three values, and is cross-listed with Many-Valued. Substructural treatments of Curry that drop contraction live in Structural/Linear or Structural/Affine by the rule they drop; their paradox motivation cross-lists them here.