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On a paraconsistentization functor in the category of consequence structures
This paper is an attempt to solve the following problem: given a logic, how
to 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 satisfying
this principle? We use a framework provided by category theory in order to
define a category of consequence structures. Then, we propose a functor to
transform a logic not able to deal with contradictions into a paraconsistent
one. Moreover, we study the case of paraconsistentization of propositional
classical logic.Comment: This new version includes corrections and a change in the order of
proposition