Connexive Logic

Connexive logic names one class of alternative, or non-classical, logics designed to exclude the so-called paradoxes of material implication. (Other logical theories with the same agenda include relevance logic, also known as relevant logic.) The characteristic that separates connexive logic from other non-classical logics is its acceptance of Aristotle's Thesis, i.e. the formula,

• ~(~p → p)

as a logical truth. Aristotle's Thesis asserts that no statement follows from its own denial. Stronger connexive logics also accept Boethius' Thesis,

• ((p → q) → ~(p → ~q))

which states that if a statement implies one thing, it does not imply its opposite.