DUBLIN — Northern Ireland’s senior appellate court overturned the murder convictions Tuesday of the only man to be convicted of the 2009 killing of two British soldiers, the latest legal setback for police and prosecutors seeking to combat Irish Republican Army splinter groups.

The three-judge Belfast court ruled that Brian Shivers’s conviction last year for murdering the two men was flawed because the trial judge had made no ruling on whether Shivers knew in advance about the attack plans.