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Logic and Logical Philosophy

Relevant Connexive Logic
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Relevant Connexive Logic

Authors

  • Nissim Francez the Technion-IIT, Haifa

DOI:

https://doi.org/10.12775/LLP.2019.007

Keywords

connexive extension of relevance logic, connexive logic, natural deduction, axiomatic system

Abstract

In this paper, a connexive extension of the Relevance logic R→ was presented. It is defined by means of a natural deduction system, and a deductively equivalent axiomatic system is presented too. The goal of such an extension is to produce a logic with stronger connection between the antecedent and the consequent of an implication.

Author Biography

Nissim Francez, the Technion-IIT, Haifa

Computer Science Deptartment

References

Anderson, Alan R., and Nuel D. Belnap Jr., Entailment, vol. 1, Princeton University Press, N.J., 1975.

Avron, Arnon, “Simple consequence relations”, Information and Computation 92 (1991): 105–139. DOI: http://dx.doi.org/10.1016/0890-5401(91)90023-U

Avron, Arnon, “Whither relevance logic”, Journal of Philosophical Logic 21, 3 (1992): 243–281. DOI: http://dx.doi.org/10.1007/BF00260930

Došen, Kosta, “The first axiomatization of relevant logic”, Journal of Philosophical Logic 21, 4 (1992): 339–356. DOI: http://dx.doi.org/10.1007/BF00260740

Dunn, J. Michael, and Greg Restall, “Relevance logic”, pages 1–136 in D.M. Gabbay and F. Guenther (eds.), Handbook of Philosophical Logic, vol. 6, 2nd edition, Kluwer, 2002. DOI: http://dx.doi.org/10.1007/978-94-017-0460-1_1

Francez, Nissim, “Natural-deduction for two connexive logics”, IfCoLog Journal of Logics and their Application 3, 3 (2016): 479–504. Special issue on Connexive Logic.

Kneale, William, and Martha Kneale, The Development of Logic, Duckworth, London, 1962.

Mares. Edwin, “Negation”, pages 180–215 in L. Horsten and R. Pettigrew (eds.), The Continuum Companion to Philosophical Logic, Continuum International Publishing Group, London, New York, 2011.

Mares, Edwin D., “Relevance and conjunction”, Journal of Logic and Computation 22 (2012): 7–21. DOI: http://dx.doi.org/10.1093/logcom/exp068

McCall, Storrs, “A history of connexivity”, pages 415–449 in D .M. Gabbay, F.J. Pelletier and J. Woods (eds.), Handbook of the History of Logic, vol. 11: “Logic: Ahistory of its central concepts”, Elsevier, Amsterdam, 2012. DOI: http://dx.doi.org/10.1016/B978-0-444-52937-4.50008-3

Omori, Hitoshi, “A simple connexive extension of the basic relevant logic BD”, IFCoLog Journal of Logic and their Applications, 3, 3 (2016): 467–b78. Special issue on Connexive Logic.

Plato, Jan Von, “Gentzen’s proof systems: Byproducts of the work of a genius”, The Bulletin of Symbolic Logic 18, 3 (2012): 313–367.

Priest, Graham, “Negation as cancellation, and connexive logic”, Topoi 18, 2 (1999): 141–148. DOI: http://dx.doi.org/10.1023/A:1006294205280

Restall, Greg, “Relevant and substructural logics”, in D. Gabbay and J. Woods (eds.), Handbook of the History of Logic, vol. 7, Logic and Modalities in the Twentieth Century, Elsevier, 2006. DOI: http://dx.doi.org/10.1016/S1874-5857(06)80030-0

Schroeder-Heister, Peter, “The categorical and the hypothetical: A critique of some fundamental assumptions of standard semantics”, Synthese 187, 3 (2012): 925–942. DOI: http://dx.doi.org/10.1007/s11229-011-9910-z

Wansing, Heinrich, “Connexive modal logic”, in R. Schmidt, I. Pratt-Hartmann, M. Reynolds and H. Wansing (eds.), Advances in Modal Logic, vol. 5, College Publications, King’s College, London, 2005.

Wansing, Heinrich, “Connexive logic”, in E.N. Zalta (ed.), The Stanford Encyclopedia of Philosophy, Fall 2014 edition, 2014. Available at

connexive/"> http://plato.stanford.edu/archives/fall2014/entries/logic-

connexive/

Logic and Logical Philosophy

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Published

2019-01-31

How to Cite

1.
FRANCEZ, Nissim. Relevant Connexive Logic. Logic and Logical Philosophy. Online. 31 January 2019. Vol. 28, no. 3, pp. 409-425. [Accessed 17 May 2025]. DOI 10.12775/LLP.2019.007.
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Vol. 28 No. 3 (2019): September

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