What is the ruling of Islam on people resorting to Bedouin traditions (salaf al-badiyah) for judgment, which include a man swearing an oath that he did not do (such-and-such), with his brothers or sons endorsing him by swearing by Allah to his truthfulness, on the condition that the phrase "to the best of our knowledge" is not uttered, otherwise the oath is invalidated?

The oath is based on the intention of the swearer, unless it involves the right of another. If it does involve the right of another, then the intention is that of the one who administers the oath, based on the saying of the Prophet, peace and blessings be upon him: "The oath is based on the intention of the one who administers it." Accordingly, if the arbitration is for the purpose of establishing or denying rights, then no one should swear an oath except in accordance with the claim of the opponent for whom the oath is sworn. If those who swear do not know the truthfulness of the one they swear to attest to, then their oath is a perjurious oath (yameen ghamoos).