Inquisitive semantics

Inquisitive semantics is a framework in logic and natural language semantics. In inquisitive semantics, the semantic content of a sentence captures both the information that the sentence conveys and the issue that it raises. The framework provides a foundation for the linguistic analysis of statements and questions. It was originally developed by Ivano Ciardelli, Jeroen Groenendijk, Salvador Mascarenhas, and Floris Roelofsen. The essential notion in inquisitive semantics is that of an inquisitive proposition. An information state (alternately a classical proposition) is a set of possible worlds. An inquisitive proposition is a nonempty downward-closed set of information states. Inquisitive propositions encode informational content via the region of logical space that their information states cover. For instance, the inquisitive proposition encodes the information that {w} is the actual world. The inquisitive proposition encodes that the actual world is either or . An inquisitive proposition encodes inquisitive content via its maximal elements, known as alternatives. For instance, the inquisitive proposition has two alternatives, namely and . Thus, it raises the issue of whether the actual world is or while conveying the information that it must be one or the other. The inquisitive proposition encodes the same information but does not raise an issue since it contains only one alternative. The informational content of an inquisitive proposition can be isolated by pooling its constituent information states as shown below. The informational content of an inquisitive proposition P is . Inquisitive propositions can be used to provide a semantics for the connectives of propositional logic since they form a Heyting algebra when ordered by the subset relation. For instance, for every proposition P there exists a relative pseudocomplement , which amounts to . Similarly, any two propositions P and Q have a meet and a join, which amount to and respectively. Thus inquisitive propositions can be assigned to formulas of as shown below.