Shevuos, Chapter 4, Mishnah 2. The Mishnah addresses the question of in which cases a person becomes obligated to bring a sacrifice for the oath of testimony, and in which cases he is exempt.
The three cases in the Mishnah:
"Chayavin al zedon hashevuah" - a person who knows testimony on behalf of his fellow, and his fellow administers an oath to him, and he deliberately swears that he does not know any testimony: he knew that he had testimony to give and nevertheless swore falsely, and he is certainly obligated to bring a sacrifice.
An unwitting oath together with awareness of the testimony - he knew that he knew testimony, but he was not aware that one who swears falsely in such a matter becomes obligated to bring a sacrifice. In this case too he is obligated.
A complete oversight - at the time of the oath he thought that he did not know any testimony, and only afterwards did he remember that he did in fact know. In this case he is exempt from the sacrifice, since at that moment he did not realize and did not think otherwise. This is how Rashi explains it.
The question of Tosafos:
Tosafos raise a difficulty with this explanation: if at the time of the oath he genuinely thought that he did not know any testimony, there is no need to arrive at an exemption based on it being unwitting, since from the outset he swore truthfully. He said, "I do not know any testimony," and at that moment this was the absolute truth, and only afterwards did he remember. If so, there is no falsehood in the oath at all, and the exemption is not because it was unwitting but because he swore truthfully.
The resolution of Tosafos:
Because of this difficulty, Tosafos explain that the oversight described in the Mishnah is not total forgetfulness. It refers to someone for whom the testimony is not at the forefront of his mind, but had he concentrated and focused his thoughts he would have remembered it. Therefore this is not an entirely truthful oath, and there is a measure of falsehood in it, since it was within his power to remember; and yet he is considered to have acted unwittingly, because at that moment he did not immediately recall that he knew the testimony.
And what is the sacrifice that one becomes obligated to bring?
In the cases where a person becomes obligated for violating the oath of testimony - whether he deliberately swore that he did not know any testimony when in fact he did, or whether he did not know that a sacrifice was involved - his obligation is a sacrifice whose value is determined in accordance with the financial situation of the one who swore.
In summary: we learned that the obligation for the oath of testimony applies both to a deliberate oath and to an unwitting oath accompanied by awareness of the testimony, whereas in a case of complete oversight he is exempt; and according to Tosafos, even this oversight is not total forgetfulness, but a temporary lapse, such that had he concentrated he would have remembered it. The sacrifice one becomes obligated to bring is a sacrifice determined according to the financial situation of the one who is obligated.