Connexive logic

<p>Connexive logic is a class of <a href="/facts/Non-classical_logic/caR36T5n">non-classical logics</a> designed to exclude the <a href="/facts/Paradoxes_of_material_implication/kIBSEESa">paradoxes of material implication</a>. The characteristic that separates connexive logic from other non-classical logics is its acceptance of Aristotle's thesis, i.e. the formula,

¬
        (
        ¬
        p
        →
        p
        )
      
    
    {\displaystyle \lnot (\lnot p\rightarrow p)}

as a <a href="/facts/Logical_truth/N0bUYhUW">logical truth</a>. Aristotle's thesis asserts that no statement <a href="/facts/Logical_consequence/AyDXp4dn">follows from</a> its own denial. Stronger connexive logics also accept Boethius' thesis,

(
        p
        →
        q
        )
        →
        ¬
        (
        p
        →
        ¬
        q
        )
      
    
    {\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.
</p><p><a href="/facts/Relevance_logic/rVQufU1b">Relevance logic</a> is another logical theory that tries to avoid the paradoxes of material implication.
</p>

Connexive logic open-in-new

Connexive logic