Paper Info
Title
The Normal and Self-extensional Extension of Dunn–Belnap Logic
Abstract
A logic $$\mathbf{L}$$ is called self-extensional if it allows to replace occurrences of a formula by occurrences of an $$\mathbf{L}$$ -equivalent one in the context of claims about logical consequence and logical validity. It is known that no three-valued paraconsistent logic which has an implication can be self-extensional. In this paper we show that in contrast, the famous Dunn–Belnap four-valued logic has (up to the choice of the primitive connectives) exactly one self-extensional four-valued extension which has an implication. We also investigate the main properties of this logic, determine the expressive power of its language (in the four-valued context), and provide a cut-free Gentzen-type proof system for it.
Year
DOI
Venue
2020
10.1007/s11787-020-00254-1
Logica Universalis
Keywords
DocType
Volume
Four-valued logics, Paraconsistent logics, Self-extensionality, Primary 03B47, Secondary 03B20
Journal
14
Issue
ISSN
Citations 
3
1661-8297
0
PageRank 
References 
Authors
0.34
0
1
Name
Order
Citations
PageRank
Arnon Avron11292147.65