Keritot, Chapter Four, Mishnah One
This mishnah returns to the subject of the asham talui. This is a guilt offering brought by one who is not sure if he transgressed.
1) If [a person was] in doubt whether he had eaten forbidden fat or not, or even if he had certainly eaten [of it] but [was] in doubt as to whether it had the requisite quantity or less; or [if there were] before him permitted fat as well as forbidden fat, and he ate of one of them and does not know of which of them he ate;
2) Or if his wife and his sister were with him in the house and he unwittingly [had sex] with one of them and does not know with which of them he unwittingly [had sex];
3) Or if he did forbidden labor and does not know whether it was on Shabbat or on a weekday,
4) He is liable for an asham talui.
Section one: These are various scenarios in which a person is not sure whether he ate forbidden fat (helev) and even if he did eat forbidden fat, he is not sure if he ate enough to make him liable for a hatat.
Section two: In this (albeit hard to imagine scenario) a man is not sure whether he had sex with his wife or sister (for whom he would be liable a hatat).
Section three: Here, he is not sure if he did the forbidden labor on Shabbat or on a weekday (perhaps he was traveling and lost track of the days of the week).
Section four: In each of these cases he cannot bring a hatat, because perhaps he did not transgress. Therefore, he brings an asham talui, which will offer him atonement in case he did transgress. If later he finds out for sure that he did transgress, then he will have to bring a hatat.