• README ⤓ .txt 2026-07-17T121634.146 000000000000768
  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.
• Ackermann Logic ⤓ .md 2026-07-15T211301.000 000000000013760
  Ackermann (1956). Rigorous implication. No paradoxes of implication. Relevance precursor. Foundation of relevant logic.
• Contraction-Free Logic ⤓ .md 2026-08-19T200646.000 000000000019760
  Grišin (1982) showed naive comprehension is consistent without contraction; Girard's linear logic (1987) made the rule's absence systematic; Restall, "How to be really contraction free" (1993); Rogerson and Restall (2004) on the residual paradoxes. No contraction rule. Resource sensitivity. Curry paradox avoidance. Foundation of substructural semantics.
• Mingle Logic ⤓ .md 2026-08-19T202407.000 000000000019648
  The matrices are Sugihara's (1955); Anderson and Belnap named and studied RM = R + mingle; Dunn (1970) proved completeness for the Sugihara algebras. Intermediate system: R ⊊ RM ⊊ classical.
• Relevance Logic ⤓ .md 2026-08-19T201130.000 000000000034576
  Ackermann's "rigorous implication" (1956). Developed extensively by Alan Anderson and Nuel Belnap (Entailment, 1975, 1992). Motivated by "paradoxes of material implication": in classical logic, A → B holds whenever A is false or B is true, regardless of connection. Relevance logic requires the antecedent be relevant to the consequent.
• Relevant Implication ⤓ .md 2026-08-19T201212.000 000000000017720
  Moh Shaw-Kwei (1950), Anderson and Belnap (1975). Antecedent must be "used" in deriving consequent. Rejects A → (B → A). Variable sharing property. Foundation for relevance logic family.
• RM3 ⤓ .md 2026-08-19T201540.000 000000000033856
  The three-element Sugihara matrix, from Sugihara's work on mingle (1955); the logic R-mingle (RM) is Anderson and Belnap's (Entailment I, 1975, §29), and RM3 is its three-valued characteristic matrix, due to Dunn (1970), who proved RM's completeness for the Sugihara algebras and RM3's role among them.
• Substructural Logics ⤓ .md 2026-07-15T053340.000 000000000028192
  Identified through Gentzen's sequent calculus (1934) by analyzing structural rules. Lambek calculus for linguistics (1958). Relevance logic (Anderson & Belnap, 1960s-70s) rejected irrelevant implications. Linear logic (Girard, 1987) rejected contraction and weakening. Unified perspective emerged recognizing the family structure.
• Ticket Entailment ⤓ .md 2026-08-19T201412.000 000000000020056
  Anderson and Belnap (1975). System T, the weakest of the main Anderson–Belnap systems: T ⊊ E ⊊ R. The name is from Ryle's "inference tickets" — a conditional is a licence to infer, not a further premise, and T is built so that only genuine ticket-uses license the arrow.
• CRITERIA ⤓ .txt 2026-07-17T121634.146 000000000000784
  Not sufficient: Variable sharing imposed as a content condition without a substructural calculus (Hyperintensional). Dropping contraction alone (Affine) or exchange alone (Ordered). A linear calculus keyed to exact resource use rather than relevance (Linear).