Abstract
This paper investigates inquisitive extensions of normal modal logic with an existential modal operator taken as primitive. The semantics of the existential modality is generalized to apply to questions, as well as statements. When the generalized existential modality is applied to a question, the result is a statement that roughly expresses that each way of resolving the question is consistent with the available information. I study the resulting logic both from a semantic and from a proof-theoretic point of view. I argue that it can be used for reasoning about a general notion of ignorance, and for reasoning about choice-offering permissions and obligations. The main technical results are sound and complete axiomatizations, both for the class of all Kripke frames, and for any class of frames corresponding to a canonical normal modal logic.
References
Aloni, M. (2007). Free choice, modals and imperatives. Natural Language Semantics, 15(1), 65–94.
Aloni, M., & Ciardelli, I. (2013). A logical account of free-choice imperatives. In M. Aloni, M. Franke, & F. Roelofsen (Eds.) The dynamic, inquisitive, and visionary life of φ, ?φ, and ♢φ: A festschrift for Jeroen Groenendijk, Martin Stokhof, and Frank Veltman (pp. 1–17). Amsterdam: ILLC Publications.
Alonso-Ovalle, L. (2006). Disjunction in alternative semantics. Ph.D. Thesis, University of Massachusetts, Amherst.
Anglberger, A., Gratzl, N., & Roy, O. (2015). Obligation, free choice, and the logic of weakest permissions. The Review of Symbolic Logic, 8(4), 807–827.
Asher, N., & Bonevac, D. (2005). Free choice permission is strong permission. Synthese, 145(3), 303–323.
Blackburn, P., de Rijke, M., & Venema, Y. (2001). Modal logic (Cambridge tracts in theoretical computer science no. 53). Cambridge: Cambridge University Press.
Blass, A., & Gurevich, Y. (2008). Program termination and well partial orderings. ACM Transactions on Computational Logic, 9(3), 1–26.
Booth, R. (2022). Independent alternatives: Ross’s puzzle and free choice. Philosophical Studies, 179, 1241–1273.
Ciardelli, I. (2016). Lifting conditionals to inquisitive semantics. In Proceedings of SALT 26 (pp. 732–752).
Ciardelli, I. (2016). Questions in logic. Ph.D. Thesis, ILLC University of Amsterdam, The Netherlands.
Ciardelli, I. (2018). Dependence statements are strict conditionals. In G. Bezhanishvili, G. D’Agostino, G. Metcalfe, & T. Studer (Eds.) Advances in modal logic (AIML) (pp. 123–142). London: College Publications.
Ciardelli, I. (2018). Questions as information types. Synthese, 195, 321–365.
Ciardelli, I., & Aloni, M. (2016). Choice-offering imperatives in inquisitive and truth-maker semantics. Presented at ‘Imperatives: worlds and beyond’, Hamburg University.
Ciardelli, I., Groenendijk, J., & Roelofsen, F. (2018). Inquisitive semantics. Oxford: Oxford University Press.
Ciardelli, I., & Roelofsen, F. (2011). Inquisitive logic. Journal of Philosophical Logic, 40(1), 55–94.
Ciardelli, I., & Roelofsen, F. (2015). Inquisitive dynamic epistemic logic. Synthese, 192, 1643–1687.
Ciardelli, I., & Roelofsen, F. (2017). Hurford’s constraint, the semantics of disjunction, and the nature of alternatives. Natural Language Semantics, 25, 199–222.
Fan, J., Wang, Y., & van Ditmarsch, H. (2015). Contingency and knowing whether. The Review of Symbolic Logic, 8(1), 75–107.
Goranko, V., & Kuusisto, A. (2018). Logics for propositional determinacy and independence. The Review of Symbolic Logic, 11(3), 470–506.
Goranko, V., & Passy, S. (1992). Using the universal modality: Gains and questions. Journal of Logic and Computation, 2(1), 5–30.
Hansson, S. O. (2013). The varieties of permission. In D. Gabbay, J. Horty, X. Parent, R. van der Meyden, & L. van der Torre (Eds.) Handbook of deontic logic and normative systems (pp. 195–240). College Publications.
Hurford, J. (1974). Exclusive or inclusive disjunction. Foundations of Language, 11(3), 409–411.
Kamp, H. (1973). Free choice permission. Proceedings of the Aristotelian Society, 74, 57–74.
Katzir, R., & Singh, R. (2013). Hurford disjunctions: embedded exhaustification and structural economy. In U. Etzeberria, A. Fălăuş, A. Irurtzun, & B. Leferman (Eds.) Proceedings of Sinn und Bedeutung 18 (pp. 201–216).
Nottelmann, N. (2016). The varieties of ignorance. In R. Peels M. Blaauw (Eds.) The epistemic dimensions of ignorance (pp. 33–56). Cambridge: Cambridge University Press.
Nygren, K. (2019). Supercover semantics for deontic action logic. Journal of Logic, Language, and Information, 28, 427–458.
Nygren, K. (2021). Deontic logic based on inquisitive semantics. In F. Liu, A. Marra, P. Portner, & F. Van De Putte (Eds.) Deontic logic and normative systems: 15th international conference, DEON 2020/2021 (pp. 339–357). London: College Publications.
Punčochář, V., & Sedlár, I. (2021). Inquisitive propositional dynamic logic. Journal of Logic, Language and Information, 30, 91–116.
Rescher, N. (2009). Ignorance: on the wider implications of deficient knowledge. Pittsburgh: University of Pittsburgh Press.
Roelofsen, F., & Uegaki, W. (2016). The distributive ignorance puzzle. In R. Truswell, C. Cummins, C. Heycock, B. Rabern, & H. Rohde (Eds.) Proceedings of Sinn und Bedeutung 21 (pp. 999–1016).
Ross, A. (1941). Imperatives and logic. Theoria, 7, 53–71.
Simons, M. (2005). Dividing things up: the semantics of or and the modal/or interaction. Natural Language Semantics, 13(3), 271–316.
Simons, M. (2005). Semantics and pragmatics in the interpretation of or. In E. Georgala J. Howell (Eds.) Proceedings of semantics and linguistic theory XV (pp. 205–222). CLC Publications, Cornell University.
Steinsvold, C. (2008). A note on logics of ignorance and borders. Notre Dame Journal of Formal Logic, 49(4), 385–392.
van der Hoek, W., & Lomuscio, A. (2004). A logic for ignorance. Electronic Notes in Theoretical Computer Science, 85(2), 117–133.
van Gessel, T. (2021). Questions in two-dimensional logic. The Review of Symbolic Logic, 1–21.
von Wright, G. H. (1968). An essay in deontic logic and the general theory of action. Amsterdam: North-Holland Publishing Company.
Acknowledgments
I would like to thank Valentin Goranko, Ivano Ciardelli, Gianluca Grilletti, Adrian Ommundsen, Ali Nosherwan Hamed, and the anonymous reviewer for helpful comments and suggestions.
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Nygren, K. Free Choice in Modal Inquisitive Logic. J Philos Logic 52, 347–391 (2023). https://doi.org/10.1007/s10992-022-09674-4
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DOI: https://doi.org/10.1007/s10992-022-09674-4
Keywords
- Inquisitive logic
- Completeness
- Free choice
- Deontic logic
- Ignorance