When the 'i' sound (as it's transliterated in English) is present in a Hebrew name, it typically means 'my' or 'of'. So the name can mean "father of judge" (the name Dan means judge), but given the cultural context of these names, it's unlikely. When a baby is born, there's no way to know what his kids are going to be like. So any name beginning Abi is going to mean "My father is" rather than "father of."