First, the central bank has the duty to warn market participants when their own behaviour is not consistent with price stability and may lead to a tightening of monetary policy which would lead to a worse outcome for all. This has to involve communication with the public at large: unions, employers, budgetary authorities.
This type of communication is in the interest of all, since any inconsistency would lead in the end to a worse result in terms of economic growth. It is also in the interest of the central bank as price stability can be more easily maintained if agents act consistently.