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This paper is an attempt to solve the following problem: given a logic, howto turn it into a paraconsistent one? In other words, given a logic in which\emph{ex falso quodlibet} holds, how to convert it into a logic not satisfyingthis principle? We use a framework provided by category theory in order todefine a category of consequence structures. Then, we propose a functor totransform a logic not able to deal with contradictions into a paraconsistentone. Moreover, we study the case of paraconsistentization of propositionalclassical logic.

On a paraconsistentization functor in the category of consequence structures