From a survey of paraconsistent logics, it appears to me that there are three main trends:(adsbygoogle = window.adsbygoogle || []).push({});

(1) Weaken implication and do away with the Axiom of Foundation in ZFC, so that the more annoying paradoxes cannot be derived. (e.g., Weber)

(2) Do away with type theory, relabeling classes as "inconsistent sets", in such a way as to allow those contradictions which previously were eliminated by type theory (e.g., Carnielli),

(3) Introduce a multi-valued logic whereby the paradoxical statements receive a new truth value (e.g., Belnap)

However, one of the reasons for interest in paraconsistent logic is not only to solve the paradoxes (which are important for Foundations but of little interest to other practicing mathematicians), but also to be able to handle information taken from humans which, for one reason or the other, ends up being contradictory. This latter style of contradiction has nothing to do with the infamous paradoxes. So it would seem that another approach is necessary than the three outlined above. Are there any? If so, I would appreciate a link that is freely accessible on the Internet. Thanks.

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# Paraconsistent logics

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