Deterministic modal Bayesian Logic: derive the Bayesian inference within the modal logic T

Frederic Dambreville

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arXiv · math/0701801

Deterministic modal Bayesian Logic: derive the Bayesian inference within the modal logic T

Frederic Dambreville

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Abstract

In 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.

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BibTeX RIS

Frederic Dambreville. 2007-01-28. Deterministic modal Bayesian Logic: derive the Bayesian inference within the modal logic T. https://arxiv.org/abs/math/0701801

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