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Logic and Logical Philosophy

Towards a bridge over two approaches in connexive logic
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Towards a bridge over two approaches in connexive logic

Authors

  • Hitoshi Omori Ruhr University Bochum

DOI:

https://doi.org/10.12775/LLP.2019.005

Keywords

connexive logic, contra-classical logic, Belnap-Dunn logic, modal logic, experimental philosophy

Abstract

The present note aims at bridging two approaches to connexive logic: one approach suggested by Heinrich Wansing, and another approach suggested by Paul Egré and Guy Politzer. To this end, a variant of FDE-based modal logic, developed by Sergei Odintsov and Heinrich Wansing, is introduced and some basic results including soundness and completeness results are established.

Author Biography

Hitoshi Omori, Ruhr University Bochum

Department of Philosophy I

References

Angell, Richard B., “A propositional logic with subjunctive conditionals”, Journal of Symbolic Logic 27, 3 (1962): 327–343. DOI: http://dx.doi.org/10.2307/2964651

Avron, Arnon, “Natural 3-valued logics characterization and proof theory”, Journal of Symbolic Logic 56, 1 (1991): 276–294. DOI: http://dx.doi.org/10.2307/2274919

Egré, Paul, and Guy Politzer, “On the negation of indicative conditionals”, pages 10–18 in M. Franke M. Aloni and F. Roelofsen (eds.), Proceedings of the Amsterdam Colloquium, 2013.

Kamide, Norihiro, and Heinrich Wansing, Proof Theory of N4-related Paraconsistent Logics, Studies in Logic, vol. 54, College Publications, London, 2015.

Kapsner, Andreas, “Strong connexivity”, Thought: A Journal of Philosophy 1, 2 (2012): 141–145. DOI: http://dx.doi.org/10.1002/tht3.19

Kapsner, Andreas, “Humble connexivity”, Logic and Logical Philosophy 28, 1 (2019). DOI: http://dx.doi.org/10.12775/LLP.2019.001

Kapsner, Andreas, and Hitoshi Omori, “Counterfactuals in Nelson Logic”, pages 497–511 in Proceedings of LORI 2017, Lecture Notes in Computer Science, 2017. DOI: http://dx.doi.org/10.1007/978-3-662-55665-8_34

McCall, Storrs, “A history of connexivity”, pages 415–449 in Handbook of the History of Logic, vol. 11, Elsevier, 2012. DOI: http://dx.doi.org/10.1016/B978-0-444-52937-4.50008-3

Odintsov, Sergei P., “The class of extensions of Nelson paraconsistent logic”, Studia Logica 80, 2–3 (2005): 291–320. DOI: http://dx.doi.org/10.1007/s11225-005-8472-9

Odintsov, Sergei P., and Heinrich Wansing, “Modal logics with Belnapian truth values”, Journal of Applied Non-Classical Logics 20, 3 (2010): 279–301. DOI: http://dx.doi.org/10.3166/jancl.20.279-304

Odintsov, Sergei P., and Heinrich Wansing, “Disentangling FDE-based paraconsistent modal logics”, Studia Logica 105, 6 (2017): 1221–1254. DOI: http://dx.doi.org/10.1007/s11225-017-9753-9

Omori, Hitoshi, “A note on Wansing’s expansion of Nelson’s logic”, Reports on Mathematical Logic 51 (2016): 133–144. DOI: http://dx.doi.org/10.4467/20842589RM.16.009.5286

Omori, Hitoshi, “A simple connexive extension of the basic relevant logic BD”, IfCoLog Journal of Logics and their Applications 3, 3 (2016): 467–478.

Omori, Hitoshi, “From paraconsistent logic to dialetheic logic”, pages 111–134 in Holger Andreas and Peter Verdée, editors, Logical Studies of Paraconsistent Reasoning in Science and Mathematics, Trends in Logic, Springer, 2016. DOI: http://dx.doi.org/10.1007/978-3-319-40220-8_8

Pfeifer, Niki, “Experiments on Aristotle’s thesis: Towards an experimental philosophy of conditionals”, The Monist 95, 2 (2012): 223–240. DOI: http://dx.doi.org/10.5840/monist201295213

Priest, Graham, An Introduction to Non-Classical Logic: From If to Is, Cambridge University Press, 2 edition, 2008. DOI: http://dx.doi.org/10.1017/CBO9780511801174

Wansing, Heinrich, “Semantics-based nonmonotonic inference”, Notre Dame Journal of Formal Logic 36, 1 (1995): 44–54. DOI: http://dx.doi.org/10.1305/ndjfl/1040308828

Wansing, Heinrich, “Negation”, pages 415–436 in L. Goble (ed.), The Blackwell Guide to Philosophical Logic, Basil Blackwell Publishers, Cambridge/MA, 2001.

Wansing, Heinrich, “Connexive modal logic”, pages 367–383 in R. Schmidt, I. Pratt-Hartmann, M. Reynolds and H. Wansing (eds.), Advances in Modal Logic, vol. 5, King’s College Publications, 2005.

Wansing, Heinrich, “Connexive logic”, in E.N. Zalta (ed.), The Stanford Encyclopedia of Philosophy. http://plato.stanford.edu/archives/fall2014/entries/logic-connexive/, Fall 2014 edition.

Wansing, Heinrich, and Daniel Skurt, “Negation as cancellation, connexive logic, and qLPm”, Australasian Journal of Logic 15, 2 (2018): 476–488. DOI: http://dx.doi.org/10.26686/ajl.v15i2.4869

Wansing, Heinrich, and Matthias Unterhuber, “Connexive conditional logic. Part I”, Logic and Logical Philosophy 28, 1 (2019). DOI: http://dx.doi.org/10.12775/LLP.2018.018

Logic and Logical Philosophy

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Published

2019-01-29

How to Cite

1.
OMORI, Hitoshi. Towards a bridge over two approaches in connexive logic. Logic and Logical Philosophy. Online. 29 January 2019. Vol. 28, no. 3, pp. 553-566. [Accessed 7 July 2025]. DOI 10.12775/LLP.2019.005.
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