Abstract: We share with some philosophers the view that a state of knowledge, being a part of the real world, can bring contradiction into it. Such an ontological reading of knowledge is very important when one deals with information knowledge, which arises as the content of the computer's memory when the computer is placed into changeable information environment ("information flow"), and "must" be able to tolerate any (not excluding contradictions) from the computer's users. Continuing research begun in [KM 93], we consider in length one kind of Scott-continuous operations introduced there. Each such operation [A->B](x), where A and B are formulas in a propositional language, called a rule, moves the computer to a "minimal" state of knowledge, in which B is true, if in a current state A is true. Note that the notion of rule is used here in an information-transforming sense, rather than in the ordinary truth-sound sense. We distinguish between global and local rules and show that these notions are decidable. Also, we define a modal epistemic logic as a tool for the prediction of possible evolution of the system's knowledge and establish decidability of this logic.