The Implications of Paraconsistency

Abstract

This is a connected scries 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. 1 Paraconsistency So many authors recently have speculated on the advantages of paraconsistent reasoning for the inference engines of intelligent systems managing large bodies of data that one hesitates to enter the lists again in support of the idea. Prominent among its champions are