Fuzzy Truth, Fuzzy Support and Fuzzy Information States for Inquisitive Semantics

In logic, the meaning of a sentence is usually reduced to its truth conditions. However, this makes sense only for declarative sentences. In order to model also the meaning of questions, inquisitive semantics replaces the truth-conditional approach relating sentences to possible worlds with a support-conditional approach that relates sentences to information states. The standard framework of inquisitive semantics is based on a crisp notion of an information state, defined as a set of possible worlds, and a crisp relation of informational support. This paper introduces and studies two refinements of the standard framework. The first refinement takes into account fuzzy information states (defined as fuzzy sets of possible worlds) and the second one introduces a notion of fuzzy informational support. The main result of this paper shows that in the resulting framework that fuzzifies inquisitive semantics in two different directions we obtain an abstract and very general version of a principle known from the basic inquisitive semantics as Truth-Support Bridge.