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PARACONSISTENT LOGICS INCLUDED IN LEWIS’ S4

Published online by Cambridge University Press:  23 July 2010

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: gemmarobles@gmail.com
UNIVERSIDAD DE SALAMANCA, EDIFICIO FES, CAMPUS UNAMUNO, 37007 SALAMANCA, SPAIN E-mail: sefus@usal.es

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
Copyright
Copyright © Association for Symbolic Logic 2010

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References

BIBLIOGRAPHY

Ackermann, W. (1956). Begründung einer strengen Implikation. Journal of Symbolic Logic, 21/2, 113128.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, 5171.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, 1522.Google Scholar
Meyer, R. K., & Routley, R. (1972). Algebraic analysis of entailment I. Logique et Analyse, 15, 407428.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), 89107.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, 357402.CrossRefGoogle Scholar
Routley, R., & Meyer, R. K. (1972). Semantics of Entailment III. Journal of Philosophical Logic, 1, 192208.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