Abstract: This paper discusses relation between three language functions (denotation, connotation, annotation) and Turing test, and points out that it is usually assumed that three language functions (denotation, connotation, annotation) are equivalent in early stage of AI research. Under such assumption, many efforts are devoted to implementing one of three language functions and suppose that one becoming true results in two others. For example, intelligence can be fully implemented through annotation function of language in Turing test. However, it has been proved that three language functions (denotation, connotation, annotation) are not equivalent, which bring great challenges to AI research. In this paper, we list some open problems in AI research, such as computational theory of dialogue.