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Term Logic
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A Note on Fernández–Coniglio’s Hierarchy of Paraconsistent Systems

Department of Logic and Methodology of Science, Institute of Philosophy, Faculty of Philosophy and History, University of Łódź, Lindleya 3/5, 90–131 Łódź, Poland
Axioms 2020, 9(2), 35; https://doi.org/10.3390/axioms9020035
Received: 8 October 2019 / Revised: 15 March 2020 / Accepted: 23 March 2020 / Published: 30 March 2020
(This article belongs to the Special Issue Deductive Systems in Traditional and Modern Logic)
A logic is called explosive if its consequence relation validates the so-called principle of ex contradictione sequitur quodlibet. A logic is called paraconsistent so long as it is not explosive. Sette’s calculus P 1 is widely recognized as one of the most important paraconsistent calculi. It is not surprising then that the calculus was a starting point for many research studies on paraconsistency. Fernández–Coniglio’s hierarchy of paraconsistent systems is a good example of such an approach. The hierarchy is presented in Newton da Costa’s style. Therefore, the law of non-contradiction plays the main role in its negative axioms. The principle of ex contradictione sequitur quodlibet has been marginalized: it does not play any leading role in the hierarchy. The objective of this paper is to present an alternative axiomatization for the hierarchy. The main idea behind it is to focus explicitly on the (in)validity of the principle of ex contradictione sequitur quodlibet. This makes the hierarchy less complex and more transparent, especially from the viewpoint of paraconsistency. View Full-Text
Keywords: paraconsistent logic; paraconsistency; Sette’s calculus; the law of explosion; the principle of ex contradictione sequitur quodlibet paraconsistent logic; paraconsistency; Sette’s calculus; the law of explosion; the principle of ex contradictione sequitur quodlibet
MDPI and ACS Style

Ciuciura, J. A Note on Fernández–Coniglio’s Hierarchy of Paraconsistent Systems. Axioms 2020, 9, 35. https://doi.org/10.3390/axioms9020035

AMA Style

Ciuciura J. A Note on Fernández–Coniglio’s Hierarchy of Paraconsistent Systems. Axioms. 2020; 9(2):35. https://doi.org/10.3390/axioms9020035

Chicago/Turabian Style

Ciuciura, Janusz. 2020. "A Note on Fernández–Coniglio’s Hierarchy of Paraconsistent Systems" Axioms 9, no. 2: 35. https://doi.org/10.3390/axioms9020035

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