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An Algebraic View of Super-Belnap Logics.

Authors :
Albuquerque, Hugo
Přenosil, Adam
Rivieccio, Umberto
Source :
Studia Logica; Dec2017, Vol. 105 Issue 6, p1051-1086, 36p
Publication Year :
2017

Abstract

The Belnap-Dunn logic (also known as First Degree Entailment, or FDE) is a well-known and well-studied four-valued logic, but until recently little has been known about its extensions, i.e. stronger logics in the same language, called super-Belnap logics here. We give an overview of several results on these logics which have been proved in recent works by Přenosil and Rivieccio. We present Hilbert-style axiomatizations, describe reduced matrix models, and give a description of the lattice of super-Belnap logics and its connections with graph theory. We adopt the point of view of Abstract Algebraic Logic, exploring applications of the general theory of algebraization of logics to the super-Belnap family. In this respect we establish a number of new results, including a description of the algebraic counterparts, Leibniz filters, and strong versions of super-Belnap logics, as well as the classification of these logics within the Leibniz and Frege hierarchies. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
00393215
Volume :
105
Issue :
6
Database :
Complementary Index
Journal :
Studia Logica
Publication Type :
Academic Journal
Accession number :
126260271
Full Text :
https://doi.org/10.1007/s11225-017-9739-7