Yes, Virginia, there really are paraconsistent logics

Journal of Philosophical Logic 28 (5):489-500 (1999)
Abstract
B. H. Slater has argued that there cannot be any truly paraconsistent logics, because it's always more plausible to suppose whatever "negation" symbol is used in the language is not a real negation, than to accept the paraconsistent reading. In this paper I neither endorse nor dispute Slater's argument concerning negation; instead, my aim is to show that as an argument against paraconsistency, it misses (some of) the target. A important class of paraconsistent logics - the preservationist logics - are not subject to this objection. In addition I show that if we identify logics by means of consequence relations, at least one dialetheic logic can be reinterpreted in preservationist (non-dialetheic) terms. Thus the interest of paraconsistent consequence relations - even those that emerge from dialetheic approaches - does not depend on the tenability of dialetheism. Of course, if dialetheism is defensible, then paraconsistent logic will be required to cope with it. But the existence (and interest) of paraconsistent logics does not depend on a defense of dialetheism
Keywords aggregation  dialetheism  paraconsistent logic  preservationism
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Reprint years 2004
DOI 10.1023/A:1004390309035
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Quine and Slater on Paraconsistency and Deviance.Francesco Paoli - 2003 - Journal of Philosophical Logic 32 (5):531-548.

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