Here’s a scenario:
Professor approaches a student about an important assignment (that could make or break a grade) and claims that the student did not turn it in (it was not in her possession). Student claims that he submitted the assignment and the teacher must have lost it. Professor believes he is lying because of the student’s past history of not turning in most assignments and not doing well in the class. Professor gives him a zero. Student later provides evidence (unprompted by the professor) to support his claim and the zero is overturned. Was it logical for the professor to conclude that the student was being “dishonest” based on missing assignments and on how well the student had performed in the course? If so, why? If not, could there have been a (logical) way for the professor to determine the truth of the student’s claim? Other thoughts on this issue are welcomed.
If the student consistently fails to turn in work, I think it is reasonable for the professor to assume that the student was lying about the XXth assignment that wasn’t turned in.
This is phrased a lot like a homework problem. 
Anyway, there are a number of questionable assumptions in the way the problem is set up.
First, the missing assignment by itself is prima facie evidence that the student did not submit the assignment. The student’s history lends support to this conclusion, but is not in itself the basis for the conclusion. Also, the question of whether the student is lying is a red herring. Integrity is a red herring. The question that must be answered is whether it is likely that the paper had in fact been submitted.
Second, you must consider burden of proof. Again, res ipsa loquitur. The professor is not obliged to prove anything, logically or not, beyond the bare fact that the paper is missing. It is up to the student to provide reasonable evidence that it was in fact submitted. The professor need only consider whether the student’s evidence meets that burden.
Third, a “determination” cannot be arrived at through logic per se. Logic can be involved, but it must be a Toulmin kind of logic, not an Aristotelian kind of logic. One can only ask what is reasonable in a situation like this, not what is “true.”