Minimal doxastic logic: probabilistic and other completeness theorems.
Peter Milne · Notre Dame Journal of Formal Logic · 1993
The propositional doxastic logics investigated here are minimal in the sense that they make very limited claims about what holds good of rational or justified belief on the basis of the meaning of those terms.Indeed some of the logics allow for the truth of total scepticism, the view that there are no rational or justified beliefs.The logics are subject to constraints such as that any doxastic logic must be believable in its own terms and that any proposition which must, according to a doxastic logic, be believed (not believed) must itself be a theorem of (be refuted by) the logic.Two techniques are used to establish completeness, one employing possible-worlds models in which there may be several or no accessibility relations, the other using probability distributions and a maximal-probability conception of belief.