Abstract
In this paper we introduce public announcements to Subset Space Logic (SSL). In order to do this we have to change the original semantics for SSL a little and consider a weaker version of SSL without the cross axiom. We present an axiomatization, prove completeness and show that this logic is PSPACE-complete. Finally, we add the arbitrary announcement modality which expresses “true after any announcement”, prove several semantic results, and show completeness for a Hilbert-style axiomatization of this logic.
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Wáng, Y.N., Ågotnes, T.: Subset Space Public Announcement Logic. In: Lodaya, K. (ed.) ICLA 2013. LNCS, vol. 7750, pp. 244–256. Springer, Heidelberg (2013)
Balbiani, P., Baltag, A., van Ditmarsch, H., Herzig, A., Hoshi, T., de Lima, T.: ‘Knowable’ as ‘known after an announcement’. The Review of Symbolic Logic 1, 305–334 (2008)
Başkent, C.: Topics in Subset Space Logic. Master Thesis of the Universiteit van Amsterdam (2007)
Başkent, C.: Public Announcement Logic in Geometric Frameworks. Fundamenta Informaticae 114, 1–17 (2012)
Blackburn, P., de Rijke, M., Venema, Y.: Modal Logic. Cambridge University Press (2001)
Dabrowski, A., Moss, L., Parikh, R.: Topological reasoning and the logic of knowledge. Annals of Pure and Applied Logic 78, 73–110 (1996)
Van Ditmarsch, H., van der Hoek, W., Kooi, B.: Dynamic Epistemic Logic. Springer (2007)
Van Ditmarsch, H., Ruan, J., Verbrugge, R.: Sum and product in dynamic epistemic logic. Journal of Logic and Computation 18, 563–588 (2008)
French, T., Van Ditmarsch, H.: Undecidability for arbitrary public announcement logic. In: Advances in Modal Logic, pp. 23–42 (2008)
Goldblatt, R.: Logics of Time and Computation. Center for the Study of Language and Computation (1992)
Halpern, J.: The effect of bounding the number of primitive propositions and the depth of nesting on the complexity of modal logic. Artificial Intelligence 65, 361–372 (1995)
Heinemann, B.: Regarding overlaps in topologic. In: AiML, vol. 6. Kings College Publications, London (2006)
Heinemann, B.: Topology and Knowledge of Multiple Agents. In: Geffner, H., Prada, R., Machado Alexandre, I., David, N. (eds.) IBERAMIA 2008. LNCS (LNAI), vol. 5290, pp. 1–10. Springer, Heidelberg (2008)
Kurucz, A.: Combining modal logics. In: Blackburn, P., van Benthem, J., Wolter, F. (eds.) Handbook of Modal Logic, pp. 869–924. Elsevier (2007)
Lutz, C.: Complexity and succinctness of public announcement logic. In: AAMAS, pp. 137–143 (2006)
Papadimitriou, C.: Computational Complexity. Addison-Wesley (1994)
Parikh, R., Moss, L., Steinsvold, C.: Topology and epistemic logic. In: Handbook of Spatial Logics, pp. 299–341. Springer (2007)
Plaza, J.: Logics of public communications. Synthese 158, 165–179 (2007)
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Balbiani, P., van Ditmarsch, H., Kudinov, A. (2013). Subset Space Logic with Arbitrary Announcements. In: Lodaya, K. (eds) Logic and Its Applications. ICLA 2013. Lecture Notes in Computer Science, vol 7750. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36039-8_21
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DOI: https://doi.org/10.1007/978-3-642-36039-8_21
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