Exhaustifying conditionals

A Mandarin conditional sentence with the form [p, jiu q], where jiu is a preverbal particle, can (but not always) convey the minimal sufficiency interpretation that nothing more — other than p — needs to be true in order for q to be true. Moreover, the exclusive focus expression zhiyao can be inserted in p without changing the minimal sufficiency interpretation. This paper proposes an exhaustification-based semantic account, according to which: (i) jiu is a special exhaustivity operator over a conditional structure, giving rise to what I call the at least component; (ii) the at least component is subject to another layer of exhaustification by a covert exhaustivity operator O, giving rise to the minimal sufficiency reading; and (iii) zhiyao is an agreement marker inside the antecedent clause which signals the existence of O at the root level. Previous accounts of conditional jiu are also reviewed and discussed.