Is it valid to classify Usul al-Din (fundamentals of religion) among the exact sciences and Usul al-Fiqh (fundamentals of Islamic jurisprudence) among the experimental sciences, and to what extent have the rules of Usul al-Fiqh remained constant over time?

Many issues in Fiqh (Islamic jurisprudence) and its Usul (principles) are based on ijtihad (independent reasoning). If a mujtahid (one who performs ijtihad) becomes strongly convinced of the preponderance of a ruling, he is obligated to act upon what his strong conviction led him to, and this then becomes definitive knowledge regarding the obligation to act upon it. Sheikh al-Islam Ibn Taymiyyah clarified the fallacy of the view that Fiqh falls under the category of conjectures (dhunun) rather than sciences (ulum), and that most of what the Mutakallimun (scholastic theologians) claim as principles (based on logic and philosophy) is neither knowledge nor sound conjecture, but rather compounded ignorance. He also mentioned that matters of creed (aqidah) can be based on strong conjecture, such as accepting a khabar al-wahid (a singular narration), because strong conjecture is considered equivalent to certain knowledge. He explained that restricting the meaning of 'knowledge' to certainty and conviction, excluding strong conjecture, is merely a terminological convention among the Mutakallimun, and contradicts the Quranic usage of 'knowledge' (ilm) to mean conjecture, citing the Almighty's saying: "And those who seek a deed of manumission from among those whom your right hands possess, then write it for them if you know any good in them" (24:33), and His saying: "They said, 'By Allah, you have certainly known that we did not come to cause corruption in the land, and we were not thieves'" (12:73).