Abstract
In this article, we introduce a logic for reasoning about probability of normative statements. We present its syntax and semantics, describe the corresponding class of models, provide an axiomatization for this logic and prove that the axiomatization is sound and complete. We also prove that our logic is decidable.
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Notes
- 1.
We might introduce \(\varDelta ^c\) and \(\varDelta ^c_\phi \) as the sets of all consistent formulas from \(\varDelta \) and \(\varDelta _\phi \), respectively, but since we will still have \(\vdash w(\phi )= \sum _{\delta \in \varDelta _\phi ^c} w(\delta )\), we prefer not to burden the notation with the superscripts in the rest of the proof, and we assume that we do not have inconsistent formulas in \(\varDelta \).
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de Wit, V., Doder, D., Meyer, J.J. (2021). A Probabilistic Deontic Logic. In: Vejnarová, J., Wilson, N. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2021. Lecture Notes in Computer Science(), vol 12897. Springer, Cham. https://doi.org/10.1007/978-3-030-86772-0_44
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