A recent major approach to deal, formally and computationally, with knowledge and belief is the AGM. We will show the adequate representation of this paradigm using three-valued model frames. AGM expansion, contraction, and revision operations, with modal epistemic formulas of a priori knowledge, a posteriori knowledge, belief, and potential knowledge are introduced. Operativity of the mentioned proposal, in an automated deduction perspective but intuition preserving, is well suited using the (Three-Valued) analytic ableaux (AT) method. Treatment of the update theory of Katsuno and Mendelzon - the other major approach - inside our framework is outlined.