On a paraconsistentization functor in the category of consequence structures. Issue 3 (2nd July 2016)

• Record Type: Journal Article
• Authors: de Souza, Edelcio G.; Costa-Leite, Alexandre; Dias, Diogo H. B.
• Is Part Of: Journal of applied non-classical logics. Volume 26:Issue 3(2016)
• Page Start: 240
• Page End: 250
• Publication Date: 2016-07-02
• Subjects: Paraconsistent logic -- functor -- category -- consequence structures; Nonclassical mathematical logic -- Periodicals; Wiskundige logica; Logic; Periodicals; 511.3105
• DOI: 10.1080/11663081.2016.1225487
• Languages: English
• ISSNs: 1166-3081

Abstract

Abstract : 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.