Cursed is he that lieth with his sister, the daughter of his father, or the daughter of his mother. - Deuteronomy 27:22
And Abraham said... She is my sister; she is the daughter of my father, but not the daughter of my mother; and she became my wife. - Genesis 20:11-12
In light of the Deutreronomic rule, and Abraham's good standing with God, is there a problem here?
Logically one could argue that there is not, since the Deuteronomic treaty took place hundreds of years after Abraham, and furthermore, Abraham was likely in a situation much like Cain's described here in which the moral hierarchy had to bend -- whereas by the time of Israel, there were many other options open.
But there's a much simpler answer than that -- if Sarah was Abraham's half-sister, it seems odd that nothing is said about this when we are told about Terah's sons earlier in Genesis. Thus is seems that this is a lie by Abraham as a way of covering himself ater being discovered: Hasn't he just finished a massive deception, and what makes the critics so sure he's telling all rightly now? (Note that Gen. 11:31 says that Sarah is Terah's daughter in law.)
-JPH