• Corpus ID: 9402750

Belief as Willingness to Bet

@article{Eijck2014BeliefAW,
  title={Belief as Willingness to Bet},
  author={Jan van Eijck and Bryan Renne},
  journal={ArXiv},
  year={2014},
  volume={abs/1412.5090}
}
We investigate modal logics of high probability having two unary modal operators: an operator $K$ expressing probabilistic certainty and an operator $B$ expressing probability exceeding a fixed rational threshold $c\geq\frac 12$. Identifying knowledge with the former and belief with the latter, we may think of $c$ as the agent's betting threshold, which leads to the motto "belief is willingness to bet." The logic $\mathsf{KB.5}$ for $c=\frac 12$ has an $\mathsf{S5}$ $K$ modality along with a… 

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