Abstract
In this paper we take the S5 definition of knowledge, and have a new look at logics combining modalities for public announcements, action models, common knowledge and relativized common knowledge. In particular, we prove two expressivity results which previously have only been shown for the case where knowledge is represented using arbitrary Kripke models but have remained open for the case of S5 models: public announcement logic with relativized common knowledge is strictly more expressive than public announcement logic with common knowledge, and action model logic with common knowledge is strictly more expressive than public announcement logic with common knowledge. We also propose and study a definition of relativized common knowledge for action model logic.
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References
Fagin, R., Halpern, J.Y., Moses, Y., Vardi, M.Y.: Reasoning about Knowledge. MIT (1995)
Meyer, J.J.C., van der Hoek, W.: Epistemic Logic for AI and Computer Science. Cambridge Tracts in Theoretical Computer Science, vol. 41. Cambridge University Press (1995)
Plaza, J.A.: Logics of public communications. In: Proceedings of ISMIS, pp. 201–216 (1989)
Baltag, A., Moss, L.S., Solecki, S.: The logic of public announcements, common knowledge, and private suspicions. In: Gilboa, I. (ed.) Proceedings of TARK, pp. 43–56 (1998)
Baltag, A., Moss, L.S.: Logics for epistemic programs. Synthese 139, 165–224 (2004)
van Benthem, J.F.A.K.: Information update as relativisation. Technical report, ILLC, University of Amsterdam (2000)
van Benthem, J.F.A.K., van Eijck, J., Kooi, B.: Logics of communication and change. Information and Computation 204, 1620–1662 (2006)
Baltag, A., Moss, L.S., Solecki, S.: Logics for epistemic actions: Completeness, decidability, expressivity (2003) (manuscript)
van Ditmarsch, H., van der Hoek, W., Kooi, B.: Dynamic Epistemic Logic. Springer (2007)
Blackburn, P., de Rijke, M., Venema, Y.: Modal Logic. Cambridge University Press (2001)
Kooi, B., van Benthem, J.: Reduction axioms for epistemic actions. In: Schmidt, R., Pratt-Hartmann, I., Reynolds, M., Wansing, H. (eds.) Advances in Modal Logic, pp. 197–211 (2004)
Kooi, B.: Expressivity and completeness for public update logics via reduction axioms. Journal of Applied Non-Classical Logics 17, 231–253 (2007)
Baltag, A.: A logic of epistemic actions. In: van der Hoek, W., Meyer, J.J.C., Witteveen, C. (eds.) Proceedings of FACAS 1999, Utrecht University (1999)
Baltag, A., Moss, L.S., Solecki, S.: The logic of public announcements, common knowledge, and private suspicions. Technical report, SEN-R9922, CWI (1999)
Wang, Y., Ågotnes, T.: Public announcement logic with distributed knowledge: expressivity, completeness and complexity. Synthese (2013), doi:10.1007/s11229-012-0243-3
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Wáng, Y.N., Ågotnes, T. (2013). Public Announcements, Private Actions and Common Knowledge in S5 Structures. In: Grossi, D., Roy, O., Huang, H. (eds) Logic, Rationality, and Interaction. LORI 2013. Lecture Notes in Computer Science, vol 8196. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40948-6_21
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DOI: https://doi.org/10.1007/978-3-642-40948-6_21
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-40947-9
Online ISBN: 978-3-642-40948-6
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