Skip to main content
×
Home
    • Aa
    • Aa

PARACONSISTENT LOGICS INCLUDED IN LEWIS’ S4

  • GEMMA ROBLES (a1) and JOSÉ M. MÉNDEZ (a2)
  • DOI: http://dx.doi.org/10.1017/S1755020310000109
  • Published online: 01 July 2010
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.

Copyright
Corresponding author
*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
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

G. Robles , & J. M Méndez . (2008). The basic constructive logic for a weak sense of consistency. Journal of Logic Language and Information, 17(1), 89107.

G. Robles , & J. M. Méndez (2009). Strong paraconsistency and the basic constructive logic for an even weaker sense of consistency. Journal of Logic, Language and Information, 18, 357402.

R. Routley , & R. K. Meyer (1972). Semantics of Entailment III. Journal of Philosophical Logic, 1, 192208.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

The Review of Symbolic Logic
  • ISSN: 1755-0203
  • EISSN: 1755-0211
  • URL: /core/journals/review-of-symbolic-logic
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×