  The special significance of meaning-rules and their relation to the meanings of expressions appears when special languages are taken into account, namely closed and connected. A language L is open if it can be extended to a new language L′ without changes in the meanings of other expressions; otherwise L is closed. A language is disconnected if there is a non-empty subset X of L such that no element of X is linked by the meaning-rules to other elements of L; otherwise, L is connected. It follows from the above definitions that if L is closed and connected, it cannot be enriched without changing the meanings of the original expressions.