On a paraconsistentization functor in the category of consequence structures
Logic
2016-06-13 v2
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 \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.
Keywords
Cite
@article{arxiv.1604.04227,
title = {On a paraconsistentization functor in the category of consequence structures},
author = {Edelcio G. de Souza and Alexandre Costa-Leite and Diogo H. B. Dias},
journal= {arXiv preprint arXiv:1604.04227},
year = {2016}
}
Comments
This new version includes corrections and a change in the order of propositions