Classical Negation and Expansions of Belnap–Dunn Logic

Studia Logica 103 (4):825-851 (2015)
  Copy   BIBTEX

Abstract

We investigate the notion of classical negation from a non-classical perspective. In particular, one aim is to determine what classical negation amounts to in a paracomplete and paraconsistent four-valued setting. We first give a general semantic characterization of classical negation and then consider an axiomatic expansion BD+ of four-valued Belnap–Dunn logic by classical negation. We show the expansion complete and maximal. Finally, we compare BD+ to some related systems found in the literature, specifically a four-valued modal logic of Béziau and the logic of classical implication and a paraconsistent de Morgan negation of Zaitsev

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,322

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

An infinity of super-Belnap logics.Umberto Rivieccio - 2012 - Journal of Applied Non-Classical Logics 22 (4):319-335.
Contradictory Information: Too Much of a Good Thing. [REVIEW]J. Michael Dunn - 2010 - Journal of Philosophical Logic 39 (4):425 - 452.
CE is not a conservative extension of E.Edwin D. Mares - 2000 - Journal of Philosophical Logic 29 (3):263-275.
Axiomatizing Belnap's conditional assertion.J. Michael Dunn - 1975 - Journal of Philosophical Logic 4 (4):383 - 397.
Relevant generalization starts here (and here = 2).Dmitry Zaitsev & Oleg Grigoriev - 2010 - Logic and Logical Philosophy 19 (4):329-340.
Classical Negation and Game-Theoretical Semantics.Tero Tulenheimo - 2014 - Notre Dame Journal of Formal Logic 55 (4):469-498.
The Logic of Conditional Negation.John Cantwell - 2008 - Notre Dame Journal of Formal Logic 49 (3):245-260.
Generalized onrno negation.J. Michael Dunn - 1996 - In Heinrich Wansing (ed.), Negation: a notion in focus. New York: W. de Gruyter. pp. 7--3.

Analytics

Added to PP
2015-01-10

Downloads
67 (#236,854)

6 months
7 (#411,145)

Historical graph of downloads
How can I increase my downloads?

Author Profiles

Citations of this work

Defining LFIs and LFUs in extensions of infectious logics.Szmuc Damian Enrique - 2016 - Journal of Applied Non-Classical Logics 26 (4):286-314.
Connexive Negation.Luis Estrada-González & Ricardo Arturo Nicolás-Francisco - 2023 - Studia Logica (Special Issue: Frontiers of Conn):1-29.

View all 20 citations / Add more citations

References found in this work

On the theory of inconsistent formal systems.Newton C. A. Costa - 1972 - Recife,: Universidade Federal de Pernambuco, Instituto de Matemática.
On the theory of inconsistent formal systems.Newton C. A. da Costa - 1974 - Notre Dame Journal of Formal Logic 15 (4):497-510.
Natural 3-valued logics—characterization and proof theory.Arnon Avron - 1991 - Journal of Symbolic Logic 56 (1):276-294.

View all 20 references / Add more references