Negation as Finite Failure is Paraconsistent

Paraconsistent logics are generally considered somewhat esoteric. Moreover, someone argued that they simply not exist, because paraconsistent negations are not negations. The aim of this work is to provide some valid reasons to reject both these assumptions. Negation as finite failure (NAF) is the standard way to compute negation, used, for instance, by all the known (to me) Prolog implementations. Despite its well-known drawbacks, it is the only effective way to compute negation in logic programming. Moreover, none has ever argued that NAF is not a “negation”, in the proper sense, although it is not a “classical negation”. It is quite simple to show that NAF exhibits paraconsistent behaviors, and this is yet another way to show that paraconsistent negations can be “true negations”. Moreover, this implies that studies on paraconsistency are not so esoteric as they can appear at a first sight: for instance, they can provide the logics community with a clean definition of what a “negation” is.