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Epistemic models of shallow depths and decision making in games: Horticulture

Published online by Cambridge University Press:  12 March 2014

Mamoru Kaneko  and
Nobu-Yuki Suzuki
Mamoru Kaneko
Affiliation:
Institute of Policy and Planning Sciences, University of Tsukuba, Ibaraki 305-8573, Japan, E-mail: [email protected]
Nobu-Yuki Suzuki
Affiliation:
Department of Mathematics, Faculty of Science, Shizuoka University, Ohya, Shizuoka 422-8529, Japan, E-mail: [email protected]
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Abstract

Kaneko-Suzuki developed epistemic logics of shallow depths with multiple players for investigations of game theoretical problems. By shallow depth, we mean that nested occurrences of belief operators of players in formulae are restricted, typically to be of finite depths, by a given epistemic structure. In this paper, we develop various methods of surgical operations (cut and paste) of epistemic world models. An example is a bouquet-making, i.e., tying several models into a bouquet. Another example is to engraft a model to some branches of another model. By these methods, we obtain various meta-theorems on semantics and syntax on epistemic logics. To illustrate possible uses of our meta-theorems, we present one game theoretical theorem, which is also a meta-theorem in the sense of logic.

Keywords

Epistemic StructureBouquet MakingCane ExtensionEngraftingEpistemic SeparationEpistemic ReductionDepth LemmaDecision Making in Games
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 68 , Issue 1 , March 2003 , pp. 163 - 186
Copyright
Copyright © Association for Symbolic Logic 2003

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References

REFERENCES

[1]Bull, R. and Segerberg, K., Basic modal logic, Handbook of philosophical logic II (Gabbay, D. and Guenthner, F., editors), Reidel, London, 1984, pp. 1–89.Google Scholar
[2]Chellas, B. F., Modal logic: an introduction, Cambridge University Press, Cambridge, 1980.CrossRefGoogle Scholar
[3]Fagin, R., Halpern, J. Y., Moses, Y., and Verdi, M. Y., Reasoning about knowledge, MIT Press, Cambridge, 1995.Google Scholar
[4]Hughes, G. E. and Cresswell, M. J., A companion to modal logic, Methuen, London, 1984.Google Scholar
[5]Kaneko, M., Epistemic logics and their game theoretical applications: Introduction, Economic Theory, vol. 19 (2002), pp. 7–62.CrossRefGoogle Scholar
[6]Kaneko, M. and Nagashima, T., Axiomatic indefinability of common knowledge in finitary logics, Epistemic logic and the theory of games and decision (Bacharach, M., Gerard-Varet, L. A., Mongin, P., and Shin, H., editors), Kluwer Academic Press, 1997, pp. 69–93.CrossRefGoogle Scholar
[7]Kaneko, M., Game logic and its applications II, Studia Logica, vol. 58 (1997), pp. 273–303.CrossRefGoogle Scholar
[8]Kaneko, M., Nagashima, T., Suzuki, N.-Y., and Tanaka, Y., A map of common knowledge logics, Studia Logica, vol. 71 (2002), pp. 57–86.CrossRefGoogle Scholar
[9]Kaneko, M. and Suzuki, N.-Y., Semantics of epistemic logics of shallow depths for game theory, IPPS. DP. 814, University of Tsukuba, 1999.Google Scholar
[10]Kaneko, M., Epistemic logics of shallow depths and game theoretical applications, to appear in Advances in modal logics, vol. 3 (Wolter, F.et al., editors), Center for the Study of Language and Information, 2001.Google Scholar
[11]Kaneko, M., Bounded interpersonal inferences and decision making, Economic Theory, vol. 19 (2002), pp. 63–103.CrossRefGoogle Scholar
[12]Meyer, J.-J. Ch and van der Hoek, W., Epistemic logic for AI and computer science, University Press, Cambridge, 1995.CrossRefGoogle Scholar
[13]Moulin, H., Game theory for the social sciences, New York University Press, New York, 1982.Google Scholar