Editing Principle of explosion (section)

==Paraconsistent logic==

[[Paraconsistent logic]]s have been developed that allow for [[subcontrary]]-forming operators. [[Formal semantics (logic)|Model-theoretic]] paraconsistent logicians often deny the assumption that there can be no model of <math>\{\phi , \lnot \phi \}</math> and devise semantical systems in which there are such models. Alternatively, they reject the idea that propositions can be classified as true or false. [[Proof-theoretic semantics|Proof-theoretic]] paraconsistent logics usually deny the validity of one of the steps necessary for deriving an explosion, typically including [[disjunctive syllogism]], [[disjunction introduction]], and ''[[reductio ad absurdum]]''.