This is where I collect and write things, mostly on academe and artificial intelligence. Established in 2010, by Vaishak Belle.
(i) It is not clear how to attach probabilities to statements containing quantifiers in a way that corresponds to the amount of conviction people have.
(ii) The information necessary to assign numerical probabilities is not ordinarily available. Therefore, a formalism that required numerical probabilities would be epistemologically inadequate.
— McCarthy and Hayes.
This argument from the 70s is a powerful one about the representational capabilities of languages for modelling reasoning systems that allow for qualitative as well as quantitative uncertainty.
It’s one of the reasons I find the work on the probabilistic situation calculus by Bacchus, Halpern and Levesque so appealing.
It allows a specification of belief that can be partial or incomplete, in keeping with whatever information is available about the application domain. It does not require specifying a prior distribution over some random variables, for example. Basically, some logical constraints are imposed on the initial state of belief. These constraints may be compatible with one or very many initial distributions and sets of independence assumptions. All the properties of belief will then follow at a corresponding level of specificity.