JTT, or other native speakers of English, let me ask this.
If I said "I think he won't come" instead of "I don't think he will come", would you think like "I see Taka puts some sort of emphasis on the nagative fact that he won't come", as JTT says? Or does it simply sound a bit weird?
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Let me reply even though I may repeat some of what Mr M said. In fact I may reapeat what I've said.
When we use, "I don't think S will ...", it is most often a first time spoken personal opinion, in other words the normal neutral whereas, "I think he won't come", sounds like someone responding, commenting further on some previous statement
![Sleep [S]](/emoticons/emotion-56.gif)
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Taka: I think he will come to the party. [= he probably will come. (could be weakened or strengthened with intonation)]
Mr M: I don't think he will come. [= he probably won't come. ( again, could be weakened or strengthened with intonation)]
MrP: I think he won't come. [ stronger than either of the first opinions because Mr P has heard both Mr M & Taka and is "overriding" them, if you will.
If there is any negation for the normal neutral situation, for English it comes in the first part. Mr P having now heard this info, is party to, or at least in his opinion he thinks he is party to some information that has him more strongly negating "his coming to the party".
Let me offer this though I may be wrong. Examples with negation in the 2nd part would be highly uncommon without some previous discussion on the issue. Have you got that? Good, explain it to me. :s