Abstract
Motivated by supplying a new strategy for connexive logic and a better semantics for conditionals so that negating a conditional amounts to negating its consequent under the condition, we propose a new semantics for connexive conditional logic, by combining Kleene’s three-valued logic and a slight modification of Stalnaker’s semantics for conditionals. In the new semantics, selection functions for selecting closest worlds for evaluating conditionals can be undefined. Truth and falsity conditions for conditionals are then supplemented with a precondition that the selection function is defined. Based on the new semantics, we define six conditional logics by different classes of models, using two notions of validity, one preserving truth and the other preserving tolerant truth. We prove soundness and completeness of these logics and compare them with some conditional logics in the literature. Our partial function plus precondition strategy may be used in other semantic frameworks to generate more connexive logics.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Adams, E. W., The Logic of Conditionals: An Application of Probability to Deductive Logic, D. Reidel, 1975.
Angell, R. B., A propositional logic with subjunctive conditionals, The Journal of Symbolic Logic 27(3):327–343, 1962.
Belnap, N. D., A useful four-valued logic, in J.M. Dunn, and G. Epstein, (eds.), Modern Uses of Multiple-Valued Logic, Springer, 1977, pp. 5–37.
Benferhat, S., D. Dubois, and H. Prade, Nonmonotonic reasoning, conditional objects and possibility theory, Artificial Intelligence 92(1):259–276, 1997.
Bennett, J., A Philosophical Guide to Conditionals, Oxford University Press, 2003.
Cantwell, J., The logic of conditional negation, Notre Dame Journal of Formal Logic 49(3):245–260, 2008.
Chellas, B. F., Basic conditional logic, Journal of Philosophical Logic 4(2):133–153, 1975.
Ciardelli, I., and X. Liu, Intuitionistic conditional logics, Journal of Philosophical Logic 49(4):807–832, 2020.
Cobreros, P., P. Egré, D. Ripley, and R. van Rooij, Tolerant, classical, strict, Journal of Philosophical Logic 41(2):347–385, 2012.
Cross, C. B., Jonathan Bennett on ‘even If’, Linguistics and Philosophy 8(3):353–357, 1985.
Günther, M., A Connexive Conditional, Logos & Episteme 13(1):55–63, 2022.
Hajek, A., Most Counterfactuals Are False, unpublished manuscript, https://philarchive.org/archive/HJEMCA, 2014.
Humberstone, L., Contra-classical logics, Australasian Journal of Philosophy 78(4):438–474, 2000.
Kapsner, A., Strong Connexivity, Thought: A Journal of Philosophy 1(2):141–145, 2012.
Kapsner, A., and H. Omori, Counterfactuals in Nelson Logic, in A. Baltag, J. Seligman, and T. Yamada, (eds.), Logic, Rationality, and Interaction, vol. 10455 of Lecture Notes in Computer Science, Springer, Berlin, Heidelberg, 2017, pp. 497–511.
Kleene, S. C., On notation for ordinal numbers, Journal of Symbolic Logic 3:150–155, 1938.
Lenzen, W., Rewriting the history of connexive logic, Journal of Philosophical Logic 51(3):525–553, 2022.
Lewis, D., Completeness and decidability of three logics of counterfactual conditionals, Theoria 37(1):74–85, 1971.
Lewis, D., Counterfactuals, Harvard University Press, 1973.
Lewis, D., Counterfactuals and comparative possibility, Journal of Philosophical Logic 2(4):418–446, 1973.
Mares, E. D., and A. Fuhrmann, A relevant theory of conditionals, Journal of Philosophical Logic 24(6):645–665, 1995.
Mccall, S., Connexive implication, The Journal of Symbolic Logic 31(3):415–433, 1966.
McCall, S., A history of connexivity, in D.M. Gabbay, F.J. Pelletier, and J. Woods, (eds.), Handbook of the History of Logic, Logic: A History of Its Central Concepts, vol. 11, North-Holland, 2012, pp. 415–449.
Nute, D., and C. B. Cross, Conditional logic, in D. Gabbay, (ed.), Handbook of Philosophical Logic, vol. 4, D. Reidel, Dordrecht, 2001, pp. 1–98.
Omori, H., From paraconsistent logic to dialetheic logic, in H. Andreas, and P. Verdée, (eds.), Logical Studies of Paraconsistent Reasoning in Science and Mathematics, vol. 45 of Trends in Logic, Springer International Publishing, Cham, 2016, pp. 111–134.
Omori, H., and H. Wansing, Connexive logics. An overview and current trends, Logic and Logical Philosophy 28(3):371–387, 2019.
Omori, H., and H. Wansing, An extension of connexive logic C, in AiML, 2020, pp. 503–522.
Pizzi, C., Boethius’ thesis and conditional logic, Journal of Philosophical Logic 6(1):283–302, 1977.
Pizzi, C., and T. Williamson, Strong Boethius’ thesis and consequential implication, Journal of Philosophical Logic 26(5):569–588, 1997.
Priest, G., The logic of paradox, Journal of Philosophical Logic 8(1):219–241, 1979.
Priest, G., Negation as cancellation, and connexive logic, Topoi 18(2):141–148, 1999.
Raidl, E., Completeness for counter-doxa conditionals—using ranking semantics, The Review of Symbolic Logic 12(4):861–891, 2019.
Raidl, E., Strengthened conditionals, in B. Liao, and Y.N. Wáng, (eds.), Context, conflict and reasoning, vol. 9 of Logic in Asia: Studia Logica Library, Springer, Singapore, 2020, pp. 139–155.
Santorio, P., Path semantics for indicative conditionals, Mind 131(521):59–98, 2022.
Stalnaker, R., A theory of conditionals, in N. Rescher, (ed.), Studies in Logical Theory, Basil Blackwell Publishers, 1968, pp. 98–112.
Stalnaker, R., and R. Thomason, A semantic analysis of conditional logic, Theoria 36(1):23–42, 1970.
Stalnaker, R. C., A defense of conditional excluded middle, in W.L. Harper, R. Stalnaker, and G. Pearce, (eds.), IFS: Conditionals, Belief, Decision, Chance and Time, The University of Western Ontario Series in Philosophy of Science, Springer Netherlands, Dordrecht, 1981, pp. 87–104.
Wansing, H., Connexive modal logic, in R. Schmidt, I. Pratt-Hartmann, M. Reynolds, and H.Wansing, (eds.), Advances in Modal Logic, Volume 5, King’s College Publications, 2005, pp. 367–383.
Wansing, H., Connexive logic, The Stanford Encyclopedia of Philosophy, 2022.
Wansing, H., and H. Omori, A Note on “A Connexive Conditional”, Logos & Episteme 13(3):325–328, 2022.
Wansing, H., and D. Skurt, Negation as cancellation, connexive logic, and qLPm, The Australasian Journal of Logic 15(2):476–488, 2018.
Wansing, H., and M. Unterhuber, Connexive conditional logic. Part I, Logic and Logical Philosophy 28(3):567–610, 2019.
Weiss, Y., Basic intuitionistic conditional logic, Journal of Philosophical Logic 48(3):447–469, 2019.
Weiss, Y., Connexive extensions of regular conditional logic, Logic and Logical Philosophy 28(3):611–627, 2019.
Weiss, Y., Did Aristotle Endorse Aristotle’s thesis? A case study in Aristotle’s Metalogic, Notre Dame Journal of Formal Logic 63(4):551–579, 2022.
Wen, X., Validity Under Assumptions, manuscript, https://doi.org/10.13140/RG.2.2.32849.45920, Jul 2021.
Willer, M., Negating Conditionals, in E. Lepore, and D. Sosa, (eds.), Oxford Studies in Philosophy of Language, Volume 2, Oxford University Press, 2022, pp. 234–266.
Williams, J. R. G., Defending Conditional Excluded Middle, Noûs 44(4):650–668, 2010.
Funding
This work was supported by the 2021 Humanities and Social Science General Program sponsored by the Ministry of Education of China (Grant No. 21YJA72040001).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Special Issue: Frontiers of Connexive Logic
Edited by: Hitoshi Omori and Heinrich Wansing
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Wen, X. Stalnakerian Connexive Logics. Stud Logica 112, 365–403 (2024). https://doi.org/10.1007/s11225-023-10043-8
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11225-023-10043-8