Boolean-valued belief functions

Some reasons are briefly sketched in favour of the idea that, besides the classical probabilistic and possibilistic measures with uncertainties quantified by real numbers from the unit interval, also non-numerical uncertainty degrees are worth being admitted, analysed and discussed. Uncertainty degrees taking their values in complete Boolean algebras are investigated in more detail, in particular when following the pattern used in the theory of belief function (known also as Dempster-Shafer theory). Rather far going and deep analogies between the usual numerical belief functions and their Boolean-valued analogies are proved to hold true.