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29 March 2024
 
  » arxiv » math/0701801

 Article overview


Deterministic modal Bayesian Logic: derive the Bayesian inference within the modal logic T
Frederic Dambreville ;
Date 28 Jan 2007
Subject Logic; Probability
AbstractIn this paper a conditional logic is defined and studied. This conditional logic, DmBL, is constructed as a deterministic counterpart to the Bayesian conditional. The logic is unrestricted, so that any logical operations are allowed. A notion of logical independence is also defined within the logic itself. This logic is shown to be non-trivial and is not reduced to classical propositions. A model is constructed for the logic. Completeness results are proved. It is shown that any unconditioned probability can be extended to the whole logic DmBL. The Bayesian conditional is then recovered from the probabilistic DmBL. At last, it is shown why DmBL is compliant with Lewis’ triviality.
Source arXiv, math/0701801
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