Abstract
This paper studies two ways of updating neighborhood models: update by taking the intersection of the neighborhoods with the announced proposition, and update by selecting all the neighborhoods that can entail the announced proposition. For each of these two ways, we establish reduction axioms and some basic model-theoretic results on public announcement logic and dynamic epistemic logic of product update. We also study various notions of group knowledge such as common and distributed knowledge over neighborhood models.
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References
Balbiani, P., van Ditmarsch, H., Kudinov, A.: Subset space logic with arbitrary announcements. In: Lodaya, K. (ed.) ICLA 2013. LNCS (LNAI), vol. 7750, pp. 233–244. Springer, Heidelberg (2013)
Baltag, A., Moss, L., Solecki, S.: The logic of public announcements, common knowledge and private suspicions. In: Proceedings of TARK, pp. 43–56. Morgan Kaufmann Publishers, Los Altos (1989)
Gasquet, O.: Completeness results in neighborhood semantics for multi-modal monotonic and regualr logics. The Journal of IGPL 4(3), 417–426 (1996)
Hansen, H.H.: Monotonic modal logic. Master’s thesis. ILLC, University of Amsterdam (2003)
Heifetz, A.: Iterative and fixed point common belief. Journal of Philosophical Logic 28, 61–79 (1999)
Holliday, W., Icard III, T.: Moorean phenomena in epistemic logic. In: Advances in Modal Logic 2010, pp. 178–199. College Publications (2010)
Lismont, L., Mongin, P.: On the logic of common belief and common knowledge. Theory and Decision 37, 75–106 (1994a)
Lismont, L., Mongin, P.: Strong completeness theorems for weak logics of common belief. Journal of Philosophical Logic 32, 115–137 (2003)
Osherson, de Jongh, D., Martin, D.E., Weinstein, S.: Formal learning theory. In: Van Benthem, J., ter Meulen, A. (eds.) Handbook of Logic and Language, pp. 737–776. Elsevier, Amsterdam (1997)
Plaza, J.: Logics of public communication. In: Proceedings of the 4th International Symposium on Methodologies for Intelligent Systems, pp. 201–206 (1989)
Van Benthem, J.: Logical Dynamics of Information and Interaction. Cambridge University Press, Cambridge (2011)
Van Benthem, J., Pacuit, E.: Dynamic logic of evidence-based belief. Studia Logica 99, 61–92 (2011)
Van Benthem, J., Sarenac, D.: The geometry of knowledge. In: Béziau, J.-Y., Leite, A., Facchini, A. (eds.) Aspects of Universal Logic, pp. 1–30. Centre de Recherches Sémiologiques, Université de Neuchatel (2004)
Van Benthem, J., Van Eijck, J., Kooi, B.: Logics of communication and change. Information and Computation 204, 1620–1662 (2006)
Van Ditmarsch, H., Van der Hoek, W., Kooi, B.: Dynamic Epistemic Logic. Springer (2008)
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Ma, M., Sano, K. (2013). How to Update Neighborhood Models. 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_16
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DOI: https://doi.org/10.1007/978-3-642-40948-6_16
Publisher Name: Springer, Berlin, Heidelberg
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