Abstract
In most modal logics, atomic propositional symbols are directly representing the meaning of sentences (such as sets of possible worlds). In other words, they use only rigid propositional designators. This means they are not able to handle uncertainty in meaning directly at the sentential level. In this paper, we offer a modal language involving non-rigid propositional designators which can also carefully distinguish de re and de dicto use of these designators. Then, we axiomatize the logics in this language with respect to all Kripke models with multiple modalities and with respect to S5 Kripke models with a single modality.
This work is supported by NSSF 22CZX066. The author also thanks the anonymous referees and the audience of the 2023 Bei**g International Summer Workshop on Formal Philosophy for their helpful comments and suggestions.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Areces, C., ten Cate, B.: 14 hybrid logics. In: Studies in Logic and Practical Reasoning, vol. 3, pp. 821–868. Elsevier (2007)
Blackburn, P., Martins, M., Manzano, M., Huertas, A.: Rigid first-order hybrid logic. In: Iemhoff, R., Moortgat, M., de Queiroz, R. (eds.) WoLLIC 2019. LNCS, vol. 11541, pp. 53–69. Springer, Heidelberg (2019). https://doi.org/10.1007/978-3-662-59533-6_4
Blumberg, K.: Counterfactual attitudes and the relational analysis. Mind 127(506), 521–546 (2018)
Blumberg, K.: Wishing, decision theory, and two-dimensional content. J. Philos. 120(2), 61–93 (2023)
Cohen, M.: Opaque updates. J. Philos. Log. 50(3), 447–470 (2021)
Cohen, M., Tang, W., Wang, Y.: De re updates. In: Halpern, J.Y., Perea, A. (eds.) Proceedings Eighteenth Conference on Theoretical Aspects of Rationality and Knowledge, TARK 2021. EPTCS, vol. 335, pp. 103–117 (2021)
Ding, Y.: On the logics with propositional quantifiers extending S5\(\Pi \). In: Bezhanishvili, G., D’Agostino, G., Metcalfe, G., Studer, T. (eds.) Advances in Modal Logic 12, pp. 219–235. College Publications (2018)
Ding, Y.: On the logic of belief and propositional quantification. J. Philos. Log. 50(5), 1143–1198 (2021)
Dorst, K.: Evidence: a guide for the uncertain. Philos. Phenomenol. Res. 100(3), 586–632 (2020)
Fine, K.: Propositional quantifiers in modal logic. Theoria 36(3), 336–346 (1970)
Fitting, M.: Modal logics between propositional and first-order. J. Log. Comput. 12(6), 1017–1026 (2002)
Fitting, M.: Types, Tableaus, and Gödel’s God, vol. 12. Springer, Science, Dordrecht (2002)
Fitting, M.: First-order intensional logic. Ann. Pure Appl. Logic 127(1–3), 171–193 (2004)
Fritz, P.: Axiomatizability of propositionally quantified modal logics on relational frames. J. Symbolic Logic, 1–38 (2022)
Gallin, D.: Intensional and Higher-Order Modal Logic. Elsevier, Amesterdam (2016)
Gallow, J.D.: Updating for externalists. Noûs 55(3), 487–516 (2021)
Gattinger, M., Wang, Y.: How to agree without understanding each other: public announcement logic with boolean definitions. In: Electronic Proceedings in Theoretical Computer Science in Proceedings TARK 2019, pp. 297, 206–220 (2019)
Halpern, J.Y., Kets, W.: A logic for reasoning about ambiguity. Artif. Intell. 209, 1–10 (2014)
Halpern, J.Y., Kets, W.: Ambiguous language and common priors. Games Econom. Behav. 90, 171–180 (2015)
Holliday, W.: A note on algebraic semantics for S5 with propositional quantifiers. Notre Dame J. Formal Logic 60(2), 311–332 (2019)
Holliday, W., Pacuit, E.: Beliefs, propositions, and definite descriptions (2016)
Kaminski, M., Tiomkin, M.: The expressive power of second-order propositional modal logic. Notre Dame J. Formal Logic 37(1), 35–43 (1996)
Kocurek, A.W.: The logic of hyperlogic. Part A: foundations. Rev. Symbolic Logic, 1–28 (2022)
Kocurek, A.W.: The logic of hyperlogic. Part B: extensions and restrictions. Rev. Symbolic Logic, 1–28 (2022)
Kooi, B.: Dynamic term-modal logic. In: van Benthem, J., Ju, S., Veltman, F. (eds.) A meeting of the minds. In: Proceedings of the Workshop on Logic, Rationality and Interaction, Bei**g, 2007, pp. 173–185. College Publications (2008)
Leitgeb, H.: Hype: a system of hyperintensional logic (with an application to semantic paradoxes). J. Philos. Log. 48(2), 305–405 (2019)
Muskens, R.: 10 higher order modal logic. In: Studies in Logic and Practical Reasoning, vol. 3, pp. 621–653. Elsevier (2007)
Ninan, D.: Imagination, content, and the self. Ph.D. thesis, Massachusetts Institute of Technology (2008)
Sedlár, I.: Hyperintensional logics for everyone. Synthese 198(2), 933–956 (2021)
Wang, Y., Wei, Y., Seligman, J.: Quantifier-free epistemic term-modal logic with assignment operator. Ann. Pure Appl. Log. 173(3), 103071 (2022)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Ding, Y. (2023). Modal Logics with Non-rigid Propositional Designators. In: Alechina, N., Herzig, A., Liang, F. (eds) Logic, Rationality, and Interaction. LORI 2023. Lecture Notes in Computer Science, vol 14329. Springer, Cham. https://doi.org/10.1007/978-3-031-45558-2_4
Download citation
DOI: https://doi.org/10.1007/978-3-031-45558-2_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-45557-5
Online ISBN: 978-3-031-45558-2
eBook Packages: Computer ScienceComputer Science (R0)
