Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-25T19:02:22.095Z Has data issue: false hasContentIssue false
  • English
  • Français

PARACONSISTENT LOGICS INCLUDED IN LEWIS’ S4

Published online by Cambridge University Press:  23 July 2010

GEMMA ROBLES  and
JOSÉ M. MÉNDEZ
GEMMA ROBLES*
Affiliation:
Dpto. de Hist. y Fil. de la CC, la Ed. y el Leng., Universidad de La Laguna
JOSÉ M. MÉNDEZ*
Affiliation:
Edificio FES, Universidad de Salamanca
*
*UNIVERSIDAD DE LA LAGUNA, EDIFICIO FACULTAD DE FILOSOFÍA, CAMPUS DE GUAJARA, 38071 LA LAGUNA, TENERIFE, SPAIN E-mail: [email protected]
†UNIVERSIDAD DE SALAMANCA, EDIFICIO FES, CAMPUS UNAMUNO, 37007 SALAMANCA, SPAIN E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

As is known, a logic S is paraconsistent if the rule ECQ (E contradictione quodlibet) is not a rule of S. Not less well known is the fact that Lewis’ modal logics are not paraconsistent. Actually, Lewis vindicates the validity of ECQ in a famous proof currently known as the “Lewis’ proof” or “Lewis’ argument.” This proof essentially leans on the Disjunctive Syllogism as a rule of inference. The aim of this paper is to define a series of paraconsistent logics included in S4 where the Disjunctive Syllogism is valid only as a rule of proof.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 3 , Issue 3 , September 2010 , pp. 442 - 466
Copyright
Copyright © Association for Symbolic Logic 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

BIBLIOGRAPHY

Ackermann, W. (1956). Begründung einer strengen Implikation. Journal of Symbolic Logic, 21/2, 113–128.CrossRefGoogle Scholar
Anderson, A. R., Belnap, N. D. Jr. (1975). Entailment. The Logic of Relevance and Necessity, Vol I. Princeton, NJ: Princeton University Press.Google Scholar
Anderson, A. R., Belnap, N. D. Jr., & Dunn, J. M. (1992). Entailment. The Logic of Relevance and Necessity, Vol II. Princeton, NJ: Princeton University Press.Google Scholar
Hacking, I. (1963). What is strict implication? Journal of Symbolic Logic, 28, 51–71.CrossRefGoogle Scholar
Lewis, C. I., & Langford, H. (1932). Symbolic Logic (Second edition). New York: Dover, 1959.Google Scholar
Méndez, J. M. (1988). Exhaustively axiomatizing S3- > and S4- > with a select list of representative theses. Bulletin of the Section of Logic, 17, 15–22.Google Scholar
Meyer, R. K., & Routley, R. (1972). Algebraic analysis of entailment I. Logique et Analyse, 15, 407–428.Google Scholar
Priest, G., & Tanaka, K. (2004). Paraconsistent logic. In Zalta, E. N., editor. The Standford Encyclopedia of Philosophy. Winter 2004 Edition. URL: http://plato.stanford.edu/archives/win2004/entries/logic-paraconsistent/.Google Scholar
Robles, G., & Méndez, J. M. (2008). The basic constructive logic for a weak sense of consistency. Journal of Logic Language and Information, 17(1), 89–107.CrossRefGoogle Scholar
Robles, G., & Méndez, J. M. (2009). Strong paraconsistency and the basic constructive logic for an even weaker sense of consistency. Journal of Logic, Language and Information, 18, 357–402.CrossRefGoogle Scholar
Routley, R., & Meyer, R. K. (1972). Semantics of Entailment III. Journal of Philosophical Logic, 1, 192–208.CrossRefGoogle Scholar
Routley, R., Meyer, R. K., Plumwood, V., & Brady, R. T. (1982a). Semantics of Entailment IV. In Routley, R., Meyer, R. K., Plumwood, V., and Brady, R. T., editors. Relevant Logics and their Rivals, Vol. 1. Atascadero, CA: Ridgeview Publishing Co., Appendix I.Google Scholar
Routley, R., Meyer, R. K., Plumwood, V., & Brady, R. T. (1982b). Relevant Logics and their Rivals, Vol. 1. Atascadero, CA: Ridgeview Publishing Co.Google Scholar
Slaney, J. K. (1995) MaGIC, Matrix Generator for Implication Connectives: Version 2.1, Notes and Guide. Canberra: Australian National University.Google Scholar