Paraconsistency in a system is usually implemented by giving semantic means to distinguish between explosive contradictions (contradictions proper) and non explosive ones (inconsistencies).
The irony is strident, the contradictions explosive.
Famous among them is ex contradictione quodlibet, also called the Law of Explosion: A ∧ ¬A → B (contradictions are "explosive" in that a conditional with a contradiction as its antecedent, and arbitrary consequent, is logically true).
(Of course, if one subscribes to the claim that entailment is explosive, a case for one contradiction is a case for all; but if entailment is paraconsistent, this argument is of no use).
In a discussion of paraconsistent logic, the primary focus is not the obtainability of contradictions but the explosive nature of a consequence relation.
Second issue was the contradiction between the upper explosive limit and vapor pressure of the crude oil vapor.
A general conception of entailment (and, by extension, a logic that captures such a conception) is explosive if, according to it, a contradiction entails everything (ex contradictione quodlibet: for all A and B: A,¬A ⊢ B).
It was exhilarating and dynamic, and also vicious and explosive.He himself was not without contradictions.
It's Ann, years later, who seems to struggle with this fatal contradiction, hoping to find what subtle but explosive impetus might have snapped something in her predecessor's mind.
A dappled glow from the explosive birth of the universe is teasing astronomers with its mysteries and apparent contradictions, as it has again and again since two scientists at Bell Laboratories in Holmdel, N.J., discovered it accidentally in 1965.
