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.
[1][2] It was originally developed by Ivano Ciardelli, Jeroen Groenendijk, Salvador Mascarenhas, and Floris Roelofsen.
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.
encodes that the actual world is either
An inquisitive proposition encodes inquisitive content via its maximal elements, known as alternatives.
For instance, the inquisitive proposition
Thus, it raises the issue of whether the actual world is
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.
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
Similarly, any two propositions P and Q have a meet and a join, which amount to
Thus inquisitive propositions can be assigned to formulas of
where W is a set of possible worlds and V is a valuation function: The operators !
are used as abbreviations in the manner shown below.
Conceptually, the !-operator can be thought of as cancelling the issues raised by whatever it applies to while leaving its informational content untouched.
, but it may differ in that it raises no nontrivial issues.
is the inquisitive proposition P from a few paragraphs ago, then
The ?-operator trivializes the information expressed by whatever it applies to, while converting information states that would establish that its issues are unresolvable into states that resolve it.
Imagine that logical space consists of four possible worlds, w1, w2, w3, and w4, and consider a formula
This proposition conveys that the actual world is either w1 or w2 and raises the issue of which of those worlds it actually is.
Therefore, the issue it raises would not be resolved if we learned that the actual world is in the information state {w3, w4}.
Rather, learning this would show that the issue raised by our toy proposition is unresolvable.