Propose, propound, pose can all mean to set before the mind for consideration.
Propose (see also INTEND ) fundamentally implies an invitation to consider, discuss, settle, or agree on some question or some proposition clearly stated or an offering for consideration or acceptance of someone as a candidate or aspirant or of something by way of a suggestion.
Propound implies the stating of a question or proposition for discussion; it usually suggests neither personal bias nor an attempt to prove or disprove on the part of the one setting it forth or in the manner of setting it forth. The term is therefore often used when the writer or speaker wishes to convey no implications of how the one propounding would answer the question or deal with the proposition.
Pose often equals propound, except that it frequently implies that no attempt will be or can be made to seek an immediate answer.