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On some remarkable relations between paraconsistent logics, modal logics, and ambiguity logics

Diderik Batens UGent (2002) LECTURE NOTES IN PURE AND APPLIED MATHEMATICS. 228. p.275-293
abstract
This paper concerns some connections between paraconsistent logics, modal logics (mainly S5), and Ambiguity Logic AL (Classical Logic applied to a language in which all letters are indexed and in which quantifiers over such indices are present). S5 may be defined from AL. Three kinds of connections will be illustrated. First, a paraconsistent logic A is presented that has the same expressive power as S5. Next, I consider the definition of paraconsistent logics from S5 and AL. Such definition is shown to work for some logics, for example Priest's LP. Other paraconsistent logics appear to withstand such definition, typically those that contain a detachable material implication. Finally, I show that some paraconsistent logics and inconsistency-adaptive logics serve exactly the same purpose as some modal logics and ampliative adaptive logics based on S5. However, they serve this purpose along very different roads and the logics cannot be defined from one another. The paper intends to open lines of research rather than pursuing them to the end. It also contains a poor person's semantics for S5 as well as a description of the simple but useful and powerful AL.
Please use this url to cite or link to this publication:
author
organization
year
type
conference (proceedingsPaper)
publication status
published
subject
in
LECTURE NOTES IN PURE AND APPLIED MATHEMATICS
editor
WA Carnielli, ME Coniglio and IML DOttaviano
volume
228
issue title
Paraconsistency : the logical way tot the inconsistent
pages
275 - 293
publisher
Marcel Dekker
place of publication
New York, NY, USA
conference name
2nd World Congress on Paraconsistency (WCP 2000)
conference location
Juquehy Sao Sebastiao, Brazil
conference start
2000-05-12
conference end
2000-05-19
Web of Science type
Proceedings Paper
Web of Science id
000179167100012
ISSN
0075-8469
ISBN
0824708059
language
English
UGent publication?
yes
classification
P1
id
402893
handle
http://hdl.handle.net/1854/LU-402893
date created
2008-05-14 16:22:00
date last changed
2017-01-02 09:52:28
@inproceedings{402893,
  abstract     = {This paper concerns some connections between paraconsistent logics, modal logics (mainly S5), and Ambiguity Logic AL (Classical Logic applied to a language in which all letters are indexed and in which quantifiers over such indices are present). S5 may be defined from AL. Three kinds of connections will be illustrated. First, a paraconsistent logic A is presented that has the same expressive power as S5. Next, I consider the definition of paraconsistent logics from S5 and AL. Such definition is shown to work for some logics, for example Priest's LP. Other paraconsistent logics appear to withstand such definition, typically those that contain a detachable material implication. Finally, I show that some paraconsistent logics and inconsistency-adaptive logics serve exactly the same purpose as some modal logics and ampliative adaptive logics based on S5. However, they serve this purpose along very different roads and the logics cannot be defined from one another. The paper intends to open lines of research rather than pursuing them to the end. It also contains a poor person's semantics for S5 as well as a description of the simple but useful and powerful AL.},
  author       = {Batens, Diderik},
  booktitle    = {LECTURE NOTES IN PURE AND APPLIED MATHEMATICS},
  editor       = {Carnielli, WA and Coniglio, ME and DOttaviano, IML},
  isbn         = {0824708059},
  issn         = {0075-8469},
  language     = {eng},
  location     = {Juquehy Sao Sebastiao, Brazil},
  pages        = {275--293},
  publisher    = {Marcel Dekker},
  title        = {On some remarkable relations between paraconsistent logics, modal logics, and ambiguity logics},
  volume       = {228},
  year         = {2002},
}

Chicago
Batens, Diderik. 2002. “On Some Remarkable Relations Between Paraconsistent Logics, Modal Logics, and Ambiguity Logics.” In Lecture Notes in Pure and Applied Mathematics, ed. WA Carnielli, ME Coniglio, and IML DOttaviano, 228:275–293. New York, NY, USA: Marcel Dekker.
APA
Batens, D. (2002). On some remarkable relations between paraconsistent logics, modal logics, and ambiguity logics. In WA Carnielli, M. Coniglio, & I. DOttaviano (Eds.), LECTURE NOTES IN PURE AND APPLIED MATHEMATICS (Vol. 228, pp. 275–293). Presented at the 2nd World Congress on Paraconsistency (WCP 2000), New York, NY, USA: Marcel Dekker.
Vancouver
1.
Batens D. On some remarkable relations between paraconsistent logics, modal logics, and ambiguity logics. In: Carnielli W, Coniglio M, DOttaviano I, editors. LECTURE NOTES IN PURE AND APPLIED MATHEMATICS. New York, NY, USA: Marcel Dekker; 2002. p. 275–93.
MLA
Batens, Diderik. “On Some Remarkable Relations Between Paraconsistent Logics, Modal Logics, and Ambiguity Logics.” Lecture Notes in Pure and Applied Mathematics. Ed. WA Carnielli, ME Coniglio, & IML DOttaviano. Vol. 228. New York, NY, USA: Marcel Dekker, 2002. 275–293. Print.