I know that もし translates to "if", but I dont know exactly when or how it should be used. I was reading Yoko Hasegawa's Japanese: a linguistic introduction. In the chapter on conditional clauses, some sentences begins with もし, others dont. Example: もし電気がついて（いれば・いたら・いる なら）、彼は家にいるだろう。versus 会員（で あれば・だったら・なら・だ と）、割引があります。(the original text is in romaji, I transcribed to hiragana for better understanding)
Since たら, なら, ば or と already express the idea of conditional, what is もし doing here? Does it have any additional function beyond those in the 4 conditional particles? If it does, what is this function, and if it doesnt, why is it included?