This question has a complicated answer, so I'll give the formal answer first. This is still in wide use, particularly in Britain, and particularly in written literature.
In formal English,and in the first person:
"shall" denotes future tense. It is synonymous with "am going to".
"should" means "ought to", and implies an obligation
"will" denotes future tense, but also implies emphasis, or a determination to succeed.
"would" denotes conditional mood, and is used for hypothetical situations.
In formal English, and in the second and third person:
"shall" denotes future tense, but also implies emphasis, or a determination to succeed.
"should" denotes conditional mood, and is used for hypothetical situations.
"will" denotes future tense. It is synonymous with "am going to".
"would" means "ought to", and implies an obligation
Modern usage, particularly in America, and particularly in spoken English, is a little bit more muddied, hence the confusion. So:
In modern, informal English, especially in America, and regardless of person:
"shall" is rarely used.
"should" means "ought to", and implies an obligation
"will" denotes future tense. It is synonymous with "am going to".
"would" denotes conditional mood, and is used for hypothetical situations.
Basically, it's a mess. In order to get it right you need to know your audience.
Rommie
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