A Poly-Connexive Logic
Keywordsconnexive logic, connexive conjunction, connexive disjunction, falsification conditions
The paper introduces a variant of connexive logic in which connexivity is extended from the interaction of negation with implication to the interaction of negation also with conjunction and disjunction. The logic is presented by two deductively equivalent methods: an axiomatic one and a natural-deduction one. Both are shown to be complete for a four-valued model theory.
Anderson, A.R., and N.Belnap Jr., Entailment, vol. 1, Princeton University Press, N.J., 1975.
Francez, N., “Natural-deduction for two connexive logics”, IfCoLog Journal of Logics and their Application 3, 3 (2016): 479–504. Special issue on Connexive Logic.
Francez, N., “Relevant connexive logic”, Logic and Logical Philosophy 28, 3 (2019): 409--425. DOI: http://dx.doi.org/10.12775/LLP.2019.007
Kamide, N., and H. Wansing, Proof Theory of N4-related Paraconsistent Logics, College Publications, London, 2015. Studies in Logic, vol. 54.
Kneale, W., and M. Kneale, The Development of Logic, Duckworth, London, 1962.
McCall, S., “A history of connexivity”, pages 415–449 in D.M. Gabbay, J.F. Pelletier and J. Woods (eds.), Handbook of the History of Logic, vol. 11, ‘Logic: a history of its central concepts”, Elsevier, Amsterdam, 2012. DOI: http://dx.doi.org/10.1016/B978-0-444-52937-4.50008-3
Olkhovikov, G.K., and P. Schroeder-Heister, “On flattening general elimination rules”, Review of Symbolic Logic 7, 1 (2014). DOI: http://dx.doi.org/10.1017/S1755020313000385
Omori, H., “A note on francez’ half-connexive formula”, IFCoLog Journal of Logic and their Applications 3, 3 (2016): 505–512. Special issue on Connexive Logic.
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.
Priest, G., “Negation as cancellation, and connexive logic”, Topoi 18, 2 (1999): 141–148. DOI: http://dx.doi.org/10.1023/A:1006294205280
Schroeder-Heister, P., “A natural extension of natural deduction”, Journal of Symbolic Logic 49 (1984): 1284–1300. DOI: http://dx.doi.org/10.2307/2274279
Schroeder-Heister, P., “The calculus of higher-level rules, propositional quantification, and the foundational approach to proof-theoretic harmony”, Studia Logica 102, 6 (2014): 1185–1216. Special issue: “Gentzen’s and Jaśkowski’s heritage: 80 Years of natural deduction and sequent calculi”, A. Indrzejczak (ed.). DOI: http://dx.doi.org/10.1007/s11225-014-9562-3
Wansing, H., “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, H., “Connexive logic”, in E.N. Zalta (ed.), The Stanford Encyclopedia of Philosophy. Fall 2014 edition, 2014. http://plato.stanford.edu/archives/fall2014/entries/logic-connexive/
Wansing, H., and M. Unterhuber, “Connexive conditional logic. Part I”, Logic and Logical Philosophy 28, 3 (2018): 567--610. DOI: http://dx.doi.org/10.12775/LLP.2018.018
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