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Logic Journal of IGPL Advance Access originally published online on July 13, 2007
Logic Journal of IGPL 2008 16(1):33-41; doi:10.1093/jigpal/jzm015
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© The Author, 2007. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

The Basic Constructive Logic for a Weak Sense of Consistency defined with a Propositional Falsity Constant

Gemma Robles

Dpto. de Historia y Filosofía de la CC, la Educación y el Languaje, Universidad de La Laguna. Campus Central, Edificio Central, 1 planta, 38201, La Laguna, Tenerife, Spain. E-mail: gemmarobles{at}gmail.com

José M. Méndez

Universidad de Salamanca, Edificio FES, Campus Unamuno, 37007, Salamanca, Spain. E-mail: sefus{at}usal.es


  Abstract

The logic BKc1 is the basic constructive logic in the ternary relational semantics (without a set of designated points) adequate to consistency understood as the absence of the negation of any theorem. Negation is introduced in BKc1 with a negation connective. The aim of this paper is to define the logic BKc1F. In this logic negation is introduced via a propositional falsity constant. We prove that BKc1 and BKc1F are definitionally equivalent.

Key Words: constructive negation • substructural logics • ternary relational semantics • definitional equivalence

Received for publication 17 May 2007.
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