This is a connected series of arguments concerning paraconsistent logic. It is argued first that paraconsistency is an option worth pursuing in automated reasoning, then that the most popular paraconsistent logic, fde, is inadequate for the reconstruction of essential first order arguments. After a case is made for regarding quantifiers as dyadic rather than monadic operators, it is shown that the addition of such quantifiers to fde allows an implication connective to be defined yielding the known logic BN4. Refining the treatment of implication in a manner similar to that found in intuitionist logic leads to the more interesting system BN.
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