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 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.
The concept of paradeduction is presented in order to justify that we can overlook contradictory information taking into account only what is consistent. Besides that, paradeduction is used to show that there is a way to transform any logic, introduced as an axiomatic formal system, into a paraconsistent one.
This paper shows how to transform explosive many-valued systems into paraconsistent logics. We investigate mainly the case of three-valued systems exhibiting how non-explosive three-valued logics can be obtained from them.
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