Abstract
This work studies positive and negative introspection not as properties, but rather as actions that change the agent’s knowledge. The actions are introduced as model update operations, with matching modalities expressing their effects. Sound and complete axiom systems are provided, and some properties are explored.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsNotes
- 1.
The paradigmatic example is \(p \wedge \lnot \mathop {\Box }{p}\).
- 2.
References
Hintikka, J.: Knowledge and Belief. Cornell University Press, Ithaca (1962)
Hendricks, V.F.: 8 bridges between formal and mainstream epistemology. Philos. Stud. 128(1), 1–5 (2006)
Fagin, R., Halpern, J.Y., Moses, Y., Vardi, M.Y.: Reasoning About Knowledge. MIT Press, Cambridge (1995)
de Bruin, B.: Explaining Games: The Epistemic Programme in Game Theory. Synthese Library, vol. 346. Springer, Dordrecht (2010). https://doi.org/10.1007/978-1-4020-9906-9
van Ditmarsch, H., French, T.: Semantics for knowledge and change of awareness. J. Logic Lang. Inf. 23(2), 169–195 (2014)
Grossi, D., Velázquez-Quesada, F.R.: Syntactic awareness in logical dynamics. Synthese 192(12), 4071–4105 (2015)
van Benthem, J., Pacuit, E.: Dynamic logics of evidence-based beliefs. Stud. Logica 99(1), 61–92 (2011)
Velázquez-Quesada, F.R.: Explicit and implicit knowledge in neighbourhood models. In: Grossi, D., Roy, O., Huang, H. (eds.) LORI 2013. LNCS, vol. 8196, pp. 239–252. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40948-6_19
Balbiani, P., Fernández-Duque, D., Lorini, E.: A logical theory of belief dynamics for resource-bounded agents. In: Jonker, C.M., Marsella, S., Thangarajah, J., Tuyls, K. (eds.) Proceedings AAMAS 2016, pp. 644–652. ACM (2016)
van Ditmarsch, H., van der Hoek, W., Kooi, B.: Dynamic Epistemic Logic. Springer, Dordrecht (2008). https://doi.org/10.1007/978-1-4020-5839-4
van Benthem, J.: Logical Dynamics of Information and Interaction. CUP, New York (2011)
van Benthem, J.: Dynamic logic for belief revision. J. Appl. Non-Class. Logics 17(2), 129–155 (2007)
van Benthem, J., Liu, F.: Dynamic logic of preference upgrade. J. Appl. Non-Class. Logics 17(2), 157–182 (2007)
Ghosh, S., Velázquez-Quesada, F.R.: Agreeing to agree: reaching unanimity via preference dynamics based on reliable agents. In: Weiss, G., Yolum, P., Bordini, R.H., Elkind, E. (eds.) Proceedings AAMAS 2015, pp. 1491–1499. ACM (2015)
Ghosh, S., Velázquez-Quesada, F.R.: A note on reliability-based preference dynamics. In: van der Hoek, W., Holliday, W.H., Wang, W. (eds.) LORI 2015. LNCS, vol. 9394, pp. 129–142. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-48561-3_11
Pucella, R., Weissman, V.: Reasoning about dynamic policies. In: Walukiewicz, I. (ed.) FoSSaCS 2004. LNCS, vol. 2987, pp. 453–467. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-24727-2_32
Göller, S.: On the complexity of reasoning about dynamic policies. In: Duparc, J., Henzinger, T.A. (eds.) CSL 2007. LNCS, vol. 4646, pp. 358–373. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-74915-8_28
Benthem, J.: An essay on sabotage and obstruction. In: Hutter, D., Stephan, W. (eds.) Mechanizing Mathematical Reasoning. LNCS (LNAI), vol. 2605, pp. 268–276. Springer, Heidelberg (2005). https://doi.org/10.1007/978-3-540-32254-2_16
Areces, C., Fervari, R., Hoffmann, G.: Moving arrows and four model checking results. In: Ong, L., de Queiroz, R. (eds.) WoLLIC 2012. LNCS, vol. 7456, pp. 142–153. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-32621-9_11
Areces, C., Fervari, R., Hoffmann, G.: Swap logic. Logic J. IGPL 22(2), 309–332 (2014)
Fervari, R.: Relation-Changing Modal Logics. Ph.D. thesis, Facultad de Matemática, Astronomía y Física, Universidad Nacional de Córdoba, Argentina (2014)
Areces, C., Fervari, R., Hoffmann, G.: Relation-changing modal operators. Logic J. IGPL 23(4), 601–627 (2015)
Kooi, B., Renne, B.: Arrow update logic. Rev. Symb. Logic 4, 536–559 (2011)
Chellas, B.F.: Modal Logic: An Introduction. Cambridge University Press, Cambridge (1980)
Blackburn, P., de Rijke, M., Venema, Y.: Modal logic. CUP, New York (2001)
Harel, D., Kozen, D., Tiuryn, J.: Dynamic Logic. MIT Press, Cambridge (2000)
van Eijck, J., Wang, Y.: Propositional dynamic logic as a logic of belief revision. In: Hodges, W., de Queiroz, R. (eds.) WoLLIC 2008. LNCS (LNAI), vol. 5110, pp. 136–148. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-69937-8_13
Prior, A.N.: Time and Modality. Clarendon Press, Oxford (1957)
Parikh, R.: The completeness of propositional dynamic logic. In: Winkowski, J. (ed.) MFCS 1978. LNCS, vol. 64, pp. 403–415. Springer, Heidelberg (1978). https://doi.org/10.1007/3-540-08921-7_88
Holliday, W., Icard, T.: Moorean phenomena in epistemic logic. In: Beklemishev, L., Goranko, V., Shehtman, V. (eds.) Advances in Modal Logic, College Publications, pp. 178–199 (2010)
Plaza, J.A.: Logics of public communications. In: Emrich, M.L., Pfeifer, M.S., Hadzikadic, M., Ras, Z.W. (eds.) Proceedings 4th International Symposium on Methodologies for Intelligent Systems, Oak Ridge National Laboratory, pp. 201–216 (1989)
van Benthem, J., van Eijck, J., Kooi, B.: Logics of communication and change. Inf. Comput. 204(11), 1620–1662 (2006)
Acknowledgements
This work was partially supported by grant ANPCyT-PICT-2013-2011, STIC-AmSud “Foundations of Graph Structured Data (FoG)”, SeCyT-UNC, the Laboratoire International Associé “INFINIS”, and the European Union’s Horizon 2020 research and innovation programme under the Marie Skodowska-Curie grant agreement No. 690974 for the project MIREL: MIning and REasoning with Legal texts.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this paper
Cite this paper
Fervari, R., Velázquez-Quesada, F.R. (2018). Dynamic Epistemic Logics of Introspection. In: Madeira, A., Benevides, M. (eds) Dynamic Logic. New Trends and Applications. DALI 2017. Lecture Notes in Computer Science(), vol 10669. Springer, Cham. https://doi.org/10.1007/978-3-319-73579-5_6
Download citation
DOI: https://doi.org/10.1007/978-3-319-73579-5_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-73578-8
Online ISBN: 978-3-319-73579-5
eBook Packages: Computer ScienceComputer Science (R0)