I am considering a paracomplete logic where the principle ¬(A∨¬A)⊢¬B holds. What does it take for the principle to be explosive, such that we can infer any ¬B?
If we have some statement that is neither true nor false in this logic, can we infer any negated proposition? That is, is a truth value gap equivalent to ¬(A∨¬A)?
Thank you.