Why LP Paraconsistent Logic is Paradoxical

In the Logic of Paradox it states that paradox is at once true and false, and the negation of a true and false statement is equivalent, giving rise to the condition for paradox, U = 0. A case can be made, however, to show that the principle of explosion, disjunctive syllogism and modus ponens can be considered to be valid. It can also be shown that the principle of non-contradiction in LP is both valid and invalid.