2019
DOI: 10.1007/s10992-019-09513-z
|View full text |Cite
|
Sign up to set email alerts
|

A Hierarchy of Classical and Paraconsistent Logics

Abstract: In this article, we will present a number of technical results concerning Classical Logic, ST and related systems. Our main contribution consists in offering a novel identity criterion for logics in general and, therefore, for Classical Logic. In particular, we will firstly generalize the ST phenomenon, thereby obtaining a recursively defined hierarchy of strict-tolerant systems. Secondly, we will prove that the logics in this hierarchy are progressively more classical, although not entirely classical. We will… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
3
1

Citation Types

0
139
0
3

Year Published

2020
2020
2023
2023

Publication Types

Select...
5
2

Relationship

1
6

Authors

Journals

citations
Cited by 60 publications
(142 citation statements)
references
References 21 publications
0
139
0
3
Order By: Relevance
“…The notion of a metainference can be generalised to cover metainferences of any order, where a metainference of order n is an arrow with metainferences of order n − 1 at each side. Barrio et al (2019) use this generalisation to prove some intriguing results. See Scambler (2019) for a rejoinder.…”
Section: Trees For Metainferencesmentioning
confidence: 90%
See 3 more Smart Citations
“…The notion of a metainference can be generalised to cover metainferences of any order, where a metainference of order n is an arrow with metainferences of order n − 1 at each side. Barrio et al (2019) use this generalisation to prove some intriguing results. See Scambler (2019) for a rejoinder.…”
Section: Trees For Metainferencesmentioning
confidence: 90%
“…5 Under the assumption that the notion of satisfaction applies equally to sequents at any metainferential level, see Scambler (2019) section 3.3 for a clarification of this point. Following Barrio et al (2019), Chris Scambler shows that there are uncountably many logics differing perhaps only at some metainferential level. A discussion of these results is beyond the scope of this paper.…”
Section: Four Three-valued Logicsmentioning
confidence: 99%
See 2 more Smart Citations
“…After all, we permit multiple conclusions in the context of inferences holding between (collections of) formulae. So, if metainferences (as argued in [4]) are inferences holding between different kinds of relata-in this case, inferences themselves-then there appears to be no reason to disallow multiple conclusions in this case but not in the other. Is there anything in particular about inferences as relata of inferences themselves that prevents us from having a unified picture, where both premises and conclusions can be sets?…”
Section: Duality For Metainferencesmentioning
confidence: 97%