  There are two main approach to probability, one of set-theoretic character
where probability is the measure of a set, and another one of linguistic
character where probability is the degree of confidence in a proposition. In
this work we give an unified algebraic treatment of these approaches through
the concept of valued lattice, obtaining as a by-product a translation between
them. Then we introduce the concept of partial valuation for DMF-algebras (De
Morgan algebras with a single fixed point for negation), giving an algebraic
setting for probability of partial events. We introduce the concept of partial
probability for propositions, substituting classical logic with Kleene's logic.
In this case too we give a translation between set-theoretic and linguistic
probability. Finally, we introduce the concept of conditional partial
probability and prove a weak form of Bayes's Theorem.
