Abstract
We introduce a multi-agent logic of knowledge with time where Fφ stands for “there is an informative event after which φ.” Formula Fφ is true in a model iff it is true in all its refinements (i.e., atoms and back are satisfied; the dual of simulation). The logic is almost normal, and positive knowledge is preserved. The meaning of Fφ is also “after the agents become aware of new factual information, φ is true,” and on finite models it is also “there is an event model (M,s) after which φ.” The former provides a correspondence with bisimulation quantifiers in a setting with epistemic operators.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Baltag, A., Moss, L.: Logics for epistemic programs. Synthese 139, 165–224 (2004); Knowledge, Rationality & Action 1–60
van Ditmarsch, H., van der Hoek, W., Kooi, B.: Dynamic Epistemic Logic. Synthese Library, vol. 337. Springer, Heidelberg (2007)
van Benthem, J., van Eijck, J., Kooi, B.: Logics of communication and change. Information and Computation 204(11), 1620–1662 (2006)
Hoshi, T.: The logic of communication graphs for group communication and the dynamic epistemic logic with a future operator. Philosophy Department, Stanford University (2006)
Balbiani, P., Baltag, A., van Ditmarsch, H., Herzig, A., Hoshi, T., Lima, T.D.: What can we achieve by arbitrary announcements? A dynamic take on Fitch’s knowability. In: Samet, D. (ed.) Proceedings of TARK XI, Louvain-la-Neuve, Belgium, pp. 42–51. Presses Universitaires de Louvain (2007)
Balbiani, P., Baltag, A., van Ditmarsch, H., Herzig, A., Hoshi, T., Lima, T.D.: ‘knowable’ as ‘known after an announcement’. Review of Symbolic Logic 1(3), 305–334 (2008)
van Benthem, J., Gerbrandy, J., Pacuit, E.: Merging frameworks for interaction: DEL and ETL. In: Samet, D. (ed.) Proceedings of TARK 2007, pp. 72–81 (2007)
Fagin, R., Halpern, J., Moses, Y., Vardi, M.: Reasoning about Knowledge. MIT Press, Cambridge (1995)
Lomuscio, A., Ryan, M.: An algorithmic approach to knowledge evolution. Artificial Intelligence for Engineering Design, Analysis and Manufacturing (AIEDAM) 13(2) (1998); Special issue on Temporal Logic in Engineering
Aczel, P.: Non-Well-Founded Sets. CSLI Lecture Notes, vol. 14. CSLI Publications, Stanford (1988)
Visser, A.: Bisimulations, model descriptions and propositional quantifiers. Logic Group Preprint Series 161, Department of Philosophy, Utrecht University (1996)
Hollenberg, M.: Logic and bisimulation. PhD thesis, University of Utrecht (1998)
French, T.: Bisimulation quantifiers for modal logic. PhD thesis, University of Western Australia (2006)
van Benthem, J., Ikegami, D.: Modal fixed-point logic and changing models. In: Avron, A., Dershowitz, N., Rabinovich, A. (eds.) Pillars of Computer Science. LNCS, vol. 4800, pp. 146–165. Springer, Heidelberg (2008); Also available as ILLC Prepublication Series PP-2008-19
French, T., van Ditmarsch, H.: Undecidability for arbitrary public announcement logic. In: Proceedings of the seventh conference “Advances in Modal Logic”, London, pp. 23–42. College Publications (2008)
Fagin, R., Halpern, J.: Belief, awareness, and limited reasoning. Artificial Intelligence 34(1), 39–76 (1988)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
van Ditmarsch, H., French, T. (2009). Simulation and Information: Quantifying over Epistemic Events. In: Meyer, JJ.C., Broersen, J. (eds) Knowledge Representation for Agents and Multi-Agent Systems. KRAMAS 2008. Lecture Notes in Computer Science(), vol 5605. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-05301-6_4
Download citation
DOI: https://doi.org/10.1007/978-3-642-05301-6_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-05300-9
Online ISBN: 978-3-642-05301-6
eBook Packages: Computer ScienceComputer Science (R0)