Luca Incurvati

According to inferential expressivism, the meaning of a logical constant is determined by the inferential relations between speech acts directed at sentences in which it occurs. Extant varieties of inferential expressivism focus exclusively on assertoric discourse, thereby neglecting the inferential role of question-directed speech acts such as asking, answering, and rejecting a question. This paper extends the inferential expressivist framework to interrogative discourse. Drawing on inquisitive semantics and the multilateralist methodology, I develop two commitment-preserving proof systems. The first, inquisitive bilateral logic (IBL), generalises assertion and weak rejection to questions as answering and withholding from answering. The second, inquisitive multilateral logic (IML), enriches IBL with force markers for accepting and rejecting a sentence, which coincide with assertion and weak rejection on declaratives but come apart for questions. This allows for a precise characterisation of asking a question as a composite commitment: accepting a question while withholding from answering it. Both systems are given a semantics via translation into systems of inquisitive modal logic and are shown to be sound and complete with respect to the corresponding notions of modal consequence.