We look at two fundamental logical processes, often intertwined in planning and problem solving: inference and update. Inference is an internal process with which we draw new conclusions, uncovering what is implicit in the information we already have. Update, on the other hand, is produced by external communication, usually in the form of announcements and in general in the form of observations, giving us information that might have been not available (even implicitly) to us before. Both processes have received attention from the logic community, usually separately. In this work, we develop a logical language that allows us to describe them together. We present syntax and semantics, as well as a complete logic for the language; we also discuss similarities and differences with other approaches, and we mention some possible ways the work can be extended.