Connexive logic

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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, $${\displaystyle \lnot (\lnot p\rightarrow p)}$$ as a logical truth. Aristotle's thesis asserts that no statement follows from its own denial. Stronger connexive logics also accept Boethius' thesis, $${\displaystyle (p\rightarrow q)\rightarrow \lnot (p\rightarrow \lnot q)}$$ which states that if a statement implies one thing, it does not imply its opposite.

Relevance logic is another logical theory that tries to avoid the paradoxes of material implication.