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A Logic for Disjunctive Ignorance

Abstract

In this paper, we introduce a notion of ‘disjunctive ignorance’, which is a weak combination of two forms of ignorance in the literature. We propose a logical language with ‘disjunctive ignorance’ as a sole modality, explore the logical properties of this notion and its related notions, and axiomatize it over various frame classes. By finding suitable reduction axioms, we extend the results to the case of public announcements and apply it to Moore-like sentences.

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Acknowledgements

This research is supported by the project 17CZX053 of National Social Science Fundation of China. The author would like to thank two anonymous referees and the editor Reinhard Muskens of this journal for their invaluable comments, which help improve the paper substantially.

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Correspondence to Jie Fan.

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Fan, J. A Logic for Disjunctive Ignorance. J Philos Logic 50, 1293–1312 (2021). https://doi.org/10.1007/s10992-021-09599-4

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  • DOI: https://doi.org/10.1007/s10992-021-09599-4

Keywords

  • Ignorance
  • Disjunctive Ignorance
  • Semi-strong non-contingency
  • Axiomatizations
  • Public announcements