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On the Transparency of Defeasible Logics: Equivalent Premise Sets, Equivalence of Their Extensions, and Maximality of the Lower Limit

Diderik Batens UGent, Christian Strasser UGent and Peter Verdée UGent (2009) Logique et Analyse. p.281-304
abstract
For Tarski logics, there are simple criteria that enable one to conclude that two premise sets are equivalent. We shall show that the very same criteria hold for adaptive logics, which is a major advantage in comparison to other approaches to defeasible reasoning forms. A related property of Tarski logics is that the extensions of equivalent premise sets with the same set of formulas are equivalent premise sets. This does not hold for adaptive logics. However a very similar criterion does. We also shall show that every monotonic logic weaker than an adaptive logic is weaker than the lower limit logic of the adaptive logic or identical to it. This highlights the role of the lower limit for settling the adaptive equivalence of extensions of equivalent premise sets.
Please use this url to cite or link to this publication:
author
organization
year
type
journalArticle (original)
publication status
published
subject
journal title
Logique et Analyse
issue
207
pages
281 - 304
publisher
Centre national belge de recherche de logique.
place of publication
Louvain
Web of Science type
article
Web of Science id
000272370300005
ISSN
0024-5836
language
English
UGent publication?
yes
classification
A1
copyright statement
I don't know the status of the copyright for this publication
id
979587
handle
http://hdl.handle.net/1854/LU-979587
date created
2010-06-16 18:11:17
date last changed
2010-06-18 14:16:15
@article{979587,
  abstract     = {For Tarski logics, there are simple criteria that enable one to conclude that two premise sets are equivalent. We shall show that the very same criteria hold for adaptive logics, which is a major advantage in comparison to other approaches to defeasible reasoning forms.

A related property of Tarski logics is that the extensions of  equivalent premise sets with the same set of formulas are equivalent premise sets. This does not hold for adaptive logics. However a very similar criterion does.

We also shall show that every monotonic logic weaker than an adaptive logic is weaker than the lower limit logic of the adaptive logic or identical to it. This highlights the role of the lower limit for settling the adaptive equivalence of extensions of equivalent premise sets.},
  author       = {Batens, Diderik and Strasser, Christian and Verd{\'e}e, Peter},
  issn         = {0024-5836},
  journal      = {Logique et Analyse},
  language     = {eng},
  number       = {207},
  pages        = {281--304},
  publisher    = {Centre national belge de recherche de logique.},
  title        = {On the Transparency of Defeasible Logics: Equivalent Premise Sets, Equivalence of Their Extensions, and Maximality of the Lower Limit},
  year         = {2009},
}

Chicago
Batens, Diderik, Christian Strasser, and Peter Verdée. 2009. “On the Transparency of Defeasible Logics: Equivalent Premise Sets, Equivalence of Their Extensions, and Maximality of the Lower Limit.” Logique Et Analyse (207): 281–304.
APA
Batens, D., Strasser, C., & Verdée, P. (2009). On the Transparency of Defeasible Logics: Equivalent Premise Sets, Equivalence of Their Extensions, and Maximality of the Lower Limit. Logique et Analyse, (207), 281–304.
Vancouver
1.
Batens D, Strasser C, Verdée P. On the Transparency of Defeasible Logics: Equivalent Premise Sets, Equivalence of Their Extensions, and Maximality of the Lower Limit. Logique et Analyse. Louvain: Centre national belge de recherche de logique.; 2009;(207):281–304.
MLA
Batens, Diderik, Christian Strasser, and Peter Verdée. “On the Transparency of Defeasible Logics: Equivalent Premise Sets, Equivalence of Their Extensions, and Maximality of the Lower Limit.” Logique et Analyse 207 (2009): 281–304. Print.