Those modals can all be used as you say, yes. James must be in India by now says The only logical conclusion is that James is now in India. James should be in India by now says It is [to be expected / quite probable] that James is now in India.
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CalifJim Not OK: It's not yet 6 o'clock; he shouldn't be home.Why not?
CalifJim Modals are very sensitive to negation. The way you used them first is how they are normally used. The 'opposite' of must is cannot.Yes, and 'needn't' can also be the opposite of 'must':
that shouldn't be a problem, right?Right. It shouldn't be, but it is.
CalifJimLoojka,I understand what you meant, just wanted to a
The original poster was asking about the modals as used in logical deduction, not the modals as used in social interactions such as obligation and freedom from obligation. For this reason, I didn't want to confuse the issue by bringing in information about the second group.
that's where my students make mistakes very oftenNot at all surprising! It's a difficult topic to master!