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Axiomatizing Rumsfeld Ignorance

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Abstract

In a recent paper, Kit Fine presents some striking results concerning the logical properties of (first-order) ignorance, second-order ignorance and Rumsfeld ignorance. However, Rumsfeld ignorance is definable in terms of ignorance, which makes some existing results and the axiomatization problem trivial. A main reason is that the accessibility relations for the implicit knowledge operator contained in the packaged operators of ignorance and Rumsfeld ignorance are the same. In this work, we assume the two accessibility relations to be different so that one of them is an arbitrary subset of the other. This will avoid the definability issue and retain most of the previous validities. The main results are axiomatizations over various proper bi-frame classes. Finally we apply our framework to analyze Fine’s results.

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Acknowledgements

This article is supported by the Fundamental Research Funds for the Central Universities. The author acknowledges two anonymous referees of this journal for their insightful and helpful comments. Special thanks go to Lloyd Humberstone and Yanjing Wang for their very helpful comments. The author also thanks three anonymous referees of NCML 2022 and the audience of that conference, where an earlier version of this article is presented.

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  1. Institute of Philosophy, Chinese Academy of Sciences, Beijing, China

    Jie Fan

  2. School of Humanities, University of Chinese Academy of Sciences, Beijing, China

    Jie Fan

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  1. Jie Fan
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Correspondence to Jie Fan.

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Fan, J. Axiomatizing Rumsfeld Ignorance. J Philos Logic 53, 79–97 (2024). https://doi.org/10.1007/s10992-023-09725-4

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