Abstract
We present a logic for reasoning about higher-order upper and lower probabilities of justification formulas. We provide sound and strongly complete axiomatization for the logic. Furthermore, we show that the introduced logic generalizes the existing probabilistic justification logic \(\mathsf {PPJ}\).
This work was supported by the SNSF project 200021\(\_\)165549 Justifications and non-classical reasoning and by the Serbian Ministry of Education and Science through Mathematical Institute of Serbian Academy of Sciences and Arts.
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Notes
- 1.
\(\mathsf {I}\) stands for iterations, \(\mathsf {LUP}\) for lower and upper probabilities and \(\mathsf {J}\) for the justification logic \(\mathsf {J}\).
- 2.
\([A]_{M,w}\) represents the set of all worlds from W(w) in a model M where A holds and will be defined later.
- 3.
When M is clear from the context we will write \([A]_w.\)
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We would like to thank the anonymous reviewers whose comments helped to improve the paper substantially.
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Doder, D., Ognjanović, Z., Savić, N., Studer, T. (2022). Incomplete Information and Justifications. In: Özgün, A., Zinova, Y. (eds) Language, Logic, and Computation. TbiLLC 2019. Lecture Notes in Computer Science, vol 13206. Springer, Cham. https://doi.org/10.1007/978-3-030-98479-3_13
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