Connexive logic

Summary

Connexive logic is a class of non-classical logics designed to exclude the paradoxes of material implication. The characteristic that separates connexive logic from other non-classical logics is its acceptance of Aristotle's thesis, i.e. the formula,

$$\lnot ( \lnot p \rightarrow p )$$

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

$$(p \rightarrow q) \rightarrow \lnot(p \rightarrow \lnot q)$$

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