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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]
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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

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