Avoiding Impossibility Theorems in Radical Inquisitive Semantics

Abstract

In nonradical inquisitive semantics, an intuitionistic Kripke model captures how group knowledge increases throughout a conversation and allows the inquisitive meaning of a sentence to be derived from its classical meaning. In radical inquisitive semantics, as proposed by Groenendijk and Roelofsen, positive and negative ways of reacting to a proposal are captured by the positive and negative inquisitive meanings of a sentence, respectively, which are inductively defined without employing any Kripke-type semantics. This paper demonstrates that, in principle, it is impossible to provide any natural Kripke-type semantics under radical inquisitive semantics. Moreover, an alternative way to establish the semantics is proposed that avoids this negative result.