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

(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:
http://hdl.handle.net/1854/LU-402893

- author
- Diderik Batens UGent
- organization
- year
- 2002
- 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.