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Logic Journal of IGPL Advance Access published online on May 6, 2008
Logic Journal of IGPL, doi:10.1093/jigpal/jzn007
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© The Author, 2008. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

The Basic Constructive Logic for Absolute Consistency defined with a Propositional Falsity Constant

Gemma Robles

Dpto. de Historia y Filosofía de la CC, la Educación y el Lenguaje, Universidad de La Laguna. Campus Central, Edificio Central, 1 planta, 38201, La Laguna, Tenerife, Spain.

E-mail: gemmarobles{at}gmail.com


  Abstract

The logic BKc6 is the basic constructive logic in the ternary relational semantics (without a set of designated points) adequate to consistency understood as absolute consistency, i.e., non-triviality. Negation is introduced in BKc6 with a negation connective. The aim of this paper is to define the logic BKc6F. In this logic negation is introduced via a propositional falsity constant. We prove that BKc6 and BKc6F are definitionally equivalent. Then, we show how to extend BKc6F within the spectrum of logics delimited by contractionless intuitionistic logic. All logics defined in the paper are paraconsistent logics.

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

Received for publication 13 January 2008.
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