Addressing The Principle
Paraconsistent logics have been developed that allow for sub-contrary forming operators. Model-theoretic paraconsistent logicians often deny the assumption that there can be no model of 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 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.
Read more about this topic: Principle Of Explosion
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