Adequate treatment of incomplete and ambiguous information encourage research in theories about reasoning and action (e. g. [7]). In [10] is proposed to deal with this topic using Belnap's four-valued logic. In this paper, Driankov's semantic is used in a formalisation that captures the dynamic character of knowledge and belief. Ambiguous knowledge is present in several kind of situations that formally corresponds with knowing that a disjunction is true, but it is not known which element of the disjunction makes it true. We define an a posteriori knowledge operator that allows to extend knowledge from ambiguous knowledge or undefined information, being in the meanwhile, potential knowledge. In addition, belief is consider local knowledge.