Abstract
Building on recent work by Yale Weiss, we study conditional logics in the intuitionistic setting. We consider a number of semantic conditions which give rise, among others, to intuitionistic counterparts of Lewis’s logic VC and Stalnaker’s C2. We show how to obtain a sound and complete axiomatization of each logic arising from a combination of these conditions. On the way, we remark how, in the intuitionistic setting, certain classically equivalent principles of conditional logic come apart, and how certain logical connections between different principles no longer hold.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Adams, E. (1965). The logic of conditionals. Inquiry, 8(1-4), 166–197.
Alechina, N., Mendler, M., De Paiva, V., Ritter, E. (2001). Categorical and Kripke semantics for constructive S4 modal logic. In Fribourg, L. (Ed.) Computer Science Logic (pp. 292–307). Berlin: Springer.
Arlo-Costa, H., Egré, P., Rott, H. (2019). The logic of conditionals. In Zalta, E.N. (Ed.) The stanford encyclopedia of philosophy. Metaphysics Research Lab, Stanford University, summer 2019 edition.
Bellin, G., De Paiva, V., Ritter, E. (2001). Extended curry-howard correspondence for a basic constructive modal logic. In Proceedings of methods for modalities, Vol. 2.
Benton, N., Bierman, G., De Paiva, V. (1998). Computational types from a logical perspective. Journal of Functional Programming, 8, 177–193.
Bezhanishvili, N., & de Jongh, D. (2006). Intuitionistic logic. Lecture Notes. Institute for Logic Language and Computation (ILLC), University of Amsterdam.
Bierman, G.M., & de Paiva, V. (2000). On an intuitionistic modal logic. Studia Logica, 65(3), 383–416.
Chellas, B. (1975). Basic conditional logic. Journal of Philosophical Logic, 4 (2), 133–153.
Ciardelli, I., & Roelofsen, F. (2011). Inquisitive logic. Journal of Philosophical Logic, 40(1), 55–94.
Ciardelli, I., Zhang, L., Champollion, L. (2018). Two switches in the theory of counterfactuals. Linguistics and Philosophy, 41(6), 577–621.
Genovese, V., Giordano, L., Gliozzi, V., Pozzato, G.L. (2014). Logics in access control: a conditional approach. Journal of Logic and Computation, 24(4), 705–762.
Kraus, S., Lehmann, D., Magidor, M. (1990). Nonmonotonic reasoning, preferential models and cumulative logics. Artificial Intelligence, 44(1-2), 167–207.
Lewis, D. (1973). Counterfactuals. Blackwell.
Nute, D. (1980). Conversational scorekeeping and conditionals. Journal of Philosophical Logic, 9(2), 153–166.
Nute, D. (1984). Conditional logic. In Handbook of philosophical logic (pp. 387–439): Springer.
de Paiva, V., & Ritter, E. (2011). Basic constructive modality. Logic without Frontiers: Festschrift for Walter Alexandre Carnielli on the occasion of his 60th Birthday, pp. 411–428.
Segerberg, K. (1989). Notes on conditional logic. Studia Logica, 48(2), 157–168.
Servi, G.F. (1981). Semantics for a class of intuitionistic modal calculi. In Dalla Chiara, M.L. (Ed.) Italian Studies in the Philosophy of Science. Studies in the Philosophy of Science, Vol. 47. Dordrecht: Springer.
Simpson, A. (1994). The proof theory and semantics of intuitionistic modal logic. Ph.D. thesis, University of Edinburgh.
Stalnaker, R. (1968). A theory of conditionals. In Rescher, N. (Ed.) Studies in Logical Theory. Blackwell, Oxford.
Stalnaker, R.C., & Thomason, R.H. (1970). A semantic analysis of conditional logic. Theoria, 36(1), 23–42.
Veltman, F. (1996). Defaults in update semantics. Journal of Philosophical Logic, 25(3), 221–261.
Weiss, Y. (2019a). Basic intuitionistic conditional logic. Journal of Philosophical Logic, 48(3), 447–469.
Weiss, Y. (2019b). Frontiers of conditional logic. Ph.D. thesis, CUNY.
Wolter, F., & Zakharyaschev, M. (1999). Intuitionistic modal logic. In Cantini, A., Casari, E., Minari, P. (Eds.) Logic and foundations of mathematics. Synthese library (Studies in epistemology, logic, methodology, and philosophy of science), Vol. 280. Dordrecht: Springer.
Acknowledgements
The authors would like to thank two anonymous reviewers for precious comments on a previous version of this paper, as well as the audience at the LoRI -VII conference in Chongqing for inspiring discussions.
Author information
Authors and Affiliations
Corresponding authors
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Ciardelli, I., Liu, X. Intuitionistic Conditional Logics. J Philos Logic 49, 807–832 (2020). https://doi.org/10.1007/s10992-019-09538-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10992-019-09538-4