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Action emulation between canonical models. (English) Zbl 1286.03049

Summary: In this paper we investigate Kripke models, used to model knowledge or belief in a static situation, and action models, used to model communicative actions that change this knowledge or belief. The appropriate notion for structural equivalence between modal structures such as Kripke models is bisimulation: Kripke models that are bisimilar are modally equivalent. We would like to find a structural relation that can play the same role for the action models that play a prominent role in information updating. Two action models are equivalent if they yield the same results when updating Kripke models. More precisely, two action models are equivalent if it holds for all Kripke models that the result of updating with one action model is bisimilar to the result of updating with the other action model. We propose a new notion of action emulation that characterizes the structural equivalence of the important class of canonical action models. Since every action model has an equivalent canonical action model, this gives a method to decide the equivalence of any pair of action models. We also give a partial result that holds for the class of all action models. Our results extend the work in [J. van Eijck et al., Synthese 185, 131–151 (2012; Zbl 1274.03030)].

MSC:

03B42 Logics of knowledge and belief (including belief change)

Citations:

Zbl 1274.03030
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References:

[1] Baltag, A., Moss, L.S., Solecki, S. (1998). The logic of public announcements, common knowledge, and private suspicions. In Proceedings of the 7th conference on theoretical aspects of rationality and knowledge (TARK ’98) (pp. 43-56). · Zbl 1386.03019
[2] Blackburn, P., de Rijke, M., Venema, Y. (2001). Modal logic. Cambridge: Cambridge University Press. · Zbl 0988.03006
[3] Sietsma, F. (2012). Logics of communication and knowledge. PhD thesis, University of Amsterdam.
[4] van Eijck, J., Ji, R., Sadzik, T. (2012). Action emulation. Synthese, 185(1), 131-151. · Zbl 1274.03030 · doi:10.1007/s11229-012-0083-1
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