Paraconsistent logic! (A reply to Slater) Jean-Yves BéziauFoot note 1_

Paraconsistent logic is the study of logics in which there are some theories embodying contradictions but which are not trivial, in particular in a paraconsistent logic, the ex contradictione sequitur quod libet, which can be formalized as Cn(T, a,¬a)=F is not valid. Since nearly half a century various systems of paraconsistent logic have been proposed and studied. This field of research is classified under a special section (B53) in the Mathematical Reviews and watching this section, it is possible to see that the number of papers devoted to paraconsistent logic is each time greater and has recently increased due in particular to its applications to computer sciences (see e.g. Blair and Subrahmanian.
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Greg Restall (2002). Paraconsistency Everywhere. Notre Dame Journal of Formal Logic 43 (3):147-156.
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