Logic Journal of IGPL

Logic Journal of IGPL Advance Access originally published online on May 6, 2008
Logic Journal of IGPL 2008 16(3):275-291; 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

The logic B_Kc6 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 B_Kc6 with a negation connective. The aim of this paper is to define the logic B_Kc6F. In this logic negation is introduced via a propositional falsity constant. We prove that B_Kc6 and B_Kc6F are definitionally equivalent. Then, we show how to extend B_Kc6F 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.

References

1. Andréka H, Madarász JX, Nemeti I. "Mutual definability does not imply definitional equivalence, a simple example". In: Mathematical Logic Quaterly (2005) 51:591–597.[CrossRef]

2. Méndez JM, Robles G. "The basic constructive logic for absolute consistency". submitted.

3. Odintsov SP. "‘Reductio ad absurdum’ and ukasiewicz's modalities". In: Logic and Logical Philosophy (2003) 11:149–166.

4. Priest G, Tanaka K. "Paraconsistent Logic". In: The Standford Encyclopedia of Philosophy—Zalta EN, ed. (2004) Winter. 2004 Edition. URL: http://plato.stanford.edu/archives/win2004/entries/logic-paraconsistent/.

5. Robles G. "The basic constructive logic for negation-consistency". In: Journal of Logic Language and Information. D.O.I. 10.1007/s10849-007-9056-z, 2008.

6. Robles G, Méndez JM. "The Basic Constructive Logic for a Weak Sense of Consistency defined with a Propositional Falsity Constant". In: Logic Journal of the IGPL (2007) doi:10.1093/jigpal/jzm015.

7. Robles G, Méndez JM. "The basic constructive logic for a weak sense of consistency". In: Journal of Logic Language and Information (2008) 17(1):89–107.[CrossRef]

8. Robles G, Méndez JM, Salto F. "Relevance logics, paradoxes of consistency and the K rule". In: Logique et Analyse (2007) 198:129–145. (An abstract of this paper was read at the Logic Colloquium 2006, Nijmegen, Holland, 27 July–2 August 2006).

9. Routley R, et al. Relevant Logics and their Rivals, Vol. 1. (1982) Atascadero, CA: Ridgeview Publishing Co.

10. J. Slaney J. MaGIC, Matrix Generator for Implication Connectives: Version 2.1, Notes and Guide. (1995) Canberra: Australian National University.

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This Article Abstract Full Text (PDF) Alert me when this article is cited Alert me if a correction is posted Services Email this article to a friend Similar articles in this journal Alert me to new issues of the journal Add to My Personal Archive Download to citation manager Request Permissions Google Scholar Articles by Robles, G. Social Bookmarking          What's this?