Part 1:
This is not my specialty, even though one of my law professors spent a good deal of time in class talking about it a few years ago, as well as it being the speciality of my aunt and uncle, so please bear with me.
Part 2:
A brief search of Google-sensei reveals that shall is used in mainly two contexts: talking about the future from the first person perspective and in legal documents to describe duty. I’ll discuss each separately and give links to further info.
Part 3:
The Future.
When talking about the future, normally it is correct to say in the first person: “I shall visit NUF,” whereas in the second or third person one would say: “you/he/she will visit NUF.” When showing strong determination, however, the two words are flipped: “I *will* visit NUF” and “you *shall* visit NUF.”
Part 4:
Legal terms.
Simply put, “shall” refers to a “duty,” whereas “will” refers to a “promise.” Think of it this way: “the party x shall clean the kitchen” means that party x *must* clean the kitchen. “Party x will clean the kitchen” means party x promises to clean the kitchen. Slightly different connotation.
"When you do hear shall in North American English, it is likely part of a legal document or conversation, where shall is fossilized with specific uses, such as indicating legal obligation."
"In the United Kingdom, however, one is more likely to hear shall for the first-person singular or plural to refer to something that is going to happen in the future, and will for the other persons."
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