What is the evidence for the permissibility of making up for intentionally breaking the fast in Ramadan, and is it based solely on analogical deduction (Qiyas), or is there another proof or a consensus (Ijma')?

According to the majority of scholars, a person who intentionally breaks their fast during the daytime in Ramadan is obligated to make up for it (qada'). If the fast was broken by sexual intercourse, expiation (kaffarah) is also required. However, if it was broken by eating, drinking, or intentionally inducing vomiting, then only qada' is necessary. This is supported by the hadith: "Whoever is overcome by vomiting while fasting does not have to make up the fast; but whoever intentionally vomits must make up the fast."

Among the other proofs is that Allah obligated qada' upon those who had a valid excuse for breaking their fast; therefore, qada' is even more incumbent upon someone who broke it intentionally, as the burden of their religious obligation has not been lifted. Ibn Abd al-Barr narrated a consensus (ijma') on the obligation of qada' for anyone who intentionally breaks their fast in Ramadan.