"He might have studied English since 2010" is possible, though it seems ambiguous whether it means continuously since 2010 or one one or more discrete occasions. If you mean the former, I would consider using "He might have been studying English since 2010" instead. I don't understand "truth but I am not sure"; it seems contradictory.
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Hans51And I was wondering if present perfect tense, which implies happenings from the past to the present can be used with auxiliary verbs?You mean 'modal verbs', not 'auxiliary verbs'. The auxiliary verb "have" obviously can indicate the present perfect; that's how you form that tense.
CalifJimI think Anna must have lived here 10 years by now.Can the above sentence be replaced by "l presume Anna have lived here 10 years by now"?
Anonymous CalifJimI think Anna must have lived here 10 years by now.Can the above sentence be replaced by "l presume Anna have lived here 10 years by now"?No, not that sentence, but if you change "have" to "has", it's OK.