Yes, the word cognitivism is derived from the word cognition. However, the word cognitivism is used in several ways. In a general sense, with respect to discourse, it is the position that sentences used in that discourse are meaningful and capable of being true or false. This concept can apply to many aspects of life, including ethics and many normative matters such as contests, music, and even the concept of democracy. All have norms (or rules), and while it would be difficult to accept that the candidate with the most delegates does not win the contest, or that C-E-G is not C Major (triad), or even that we have freedom of speech, the contrast in ethics can be true or false too. We may want ethical statements to be categorically true, while we only need statements about right action to be contingent on the acceptance of the rules of a situation. The choice to play the contest, compose or conceptualize music, pursue the lawful promise that is America according to the given set of rules are all legitimate transfers of application.
I admit, while it does not reflect an absolute, it does reflect an abated position or diminution which lies somewhere inbetween. Thus, limited cognitivism does not adhere to the rules, nor to the concept of absolutes. In short, artistic license.