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Intent can be relevant in immigration. For example, if you intend to engage in certain activities, you may require a different kind of visa. In almost any country, entering as a visitor requires an intent to leave before the end of the authorized period of stay.
To the extent that your intent may be relevant to a visa application, you should absolutely state your intent. That this is something you could lie about is not lost on most visa officers, but your statement about your intent is nonetheless evidence. If you don't make the statement, you open up the possibility of the officer saying that there's insufficient evidence of your intention.
So, if you are asked to describe the purpose of a two-week tourist trip, for example, your statement that you plan to visit for two weeks for tourism is a statement of your intent, and it is crucial evidence for the visa officer.
Of course, visa officers will not necessarily take your statements at face value. Instead, they will evaluate your credibility and view your statements in light of the credibility determination. Anyone who makes a statement of their own intent and then attempts to use it as incontrovertible proof of some position is going to lose credibility, not gain it. So just say what was on your mind and leave it at that.
Another factor visa officers will usually consider, of course, is consistency. If you have other evidence that supports your statements of intent, that will improve the officer's view of your credibility.
Without knowing what specific intent is being called into question, it's difficult to know with more certainty what to tell you. Since you're asking about prior refusals, I would note that you probably shouldn't make claims about the prior refusals having been incorrect. That is, if the refusal said that you hadn't established your intent to leave the country at the end of your visit, don't argue in this application that you actually had such an intent in that refused application. Just use this application to show that you have that intent now. (In fact, most refusals don't say that they think you intend not to leave, they just say that you failed to convince them that you have an intent to leave. The difference is subtle but important.)
Now that you have added some more information to the question, I would note that US refusals don't give case-specific reasons. Therefore, there is no way to know whether the refusal was caused by the officer doubting your stated plan to attend the convention. I suppose it probably wasn't.
All you can know about why you were refused is the specific section of law that was cited in your refusal notice. It probably doesn't make much difference whether you explain the reason for your earlier visa application (perhaps unless it's particularly relevant to your current application). In any event, the visa officer probably has access to your original application, in which case she or he knows what you said about why you made the application, as well as knowing more about the reasons for that refusal than you ever will.
Upvote:3
You must answer the questions asked in the application. You should answer truthfully and completely, remembering that you are not required to answer questions that aren't asked.
Thus, the answer to your question here is you don't have to mention your earlier intent unless the application asks about it. If you think that mentioning it will improve this application by allowing the visa officer to see inside your mind, then you're free to do so.
Without knowing every detail of your application and personal history, it's impossible to make a general answer. I would suggest, however, that the visa officer is more interested in the details of this application than in second- or third-level matters related to a previous one.