I agree with the person who claimed that this inscription gives the man's name as Abba ben Abba (which would indeed mean that the father had died between the son's conception and his birth).
Contrary to an earlier suggestion, the name Abba has no connection with Abraham; indeed it appears nowhere in the Bible. But it is a very common name of many rabbis mentioned in the Talmud. However, I would point out that Abba is always transliterated with two "b"s. That's because the letter bet in the name Abba contains a *dagesh hazaq* ("strong stress-dot") -- which is Hebrew's way of indicating a doubled consonant (I won't bore you with the grammatical reasons.) We don't actually see the *dagesh* in the letter bet, because tombstone inscriptions show only the consonants. But it is in fact a "double-bet"-- hence must be spelled with two "b"s in Latin alphabet transliteration.
