This paper presents a tableaux calculus for the Propositional Logic of Contexts with the ist(c,¢) modality. This approach has a twofold advantage: from the user viewpoint it presents rules which intuitively reflect epistemic properties (lifting, use of assumptions etc.); from a computational perspective it allows local and incremental computation, satisfies strong confluence and can therefore be adapted efficiently to different search heuristics. The modelling of contexts as partial objects is obtained by using superficial assignments. We can define meaningful and meaningless sentences and reason about formulae containing both kind of sentences. Superficial valuations provide us with a sound and incremental approximation of classical logic and make it possible to present a simplified semantics based on layered models.