The Review of Symbolic Logic

Research Article

PARACONSISTENT LOGICS INCLUDED IN LEWIS’ S4

GEMMA ROBLESa1 c1 and JOSÉ M. MÉNDEZa2 c2

a1 Dpto. de Hist. y Fil. de la CC, la Ed. y el Leng., Universidad de La Laguna

a2 Edificio FES, Universidad de Salamanca

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.

(Received July 25 2009)

Correspondence:

c1 UNIVERSIDAD DE LA LAGUNA, EDIFICIO FACULTAD DE FILOSOFÍA, CAMPUS DE GUAJARA, 38071 LA LAGUNA, TENERIFE, SPAIN E-mail: gemmarobles@gmail.com

c2 UNIVERSIDAD DE SALAMANCA, EDIFICIO FES, CAMPUS UNAMUNO, 37007 SALAMANCA, SPAIN E-mail: sefus@usal.es